Actually, that's a sort of oversimplification.
The way feedback relates to "sound" is actually somewhat complex - and it's quite different depending on whether you're talking about preamps or power amps.
Unless it's designed to specifically be otherwise, a tube preamp won't have much "tube sound". Most well-designed tube preamps are relatively flat and have relatively low distortion. (The second harmonic distortion that causes the characteristic "sweetness" will be there - but only a tiny bit of it; the bass may be somewhat rolled off and a little less well controlled than with a solid state unit, but that won't be that obvious either. Serious bass rolloff is certainly possible, but easily avoided by careful design.) Adding feedback on a typical tube preamp (capacitor coupled or direct coupled) actually won't have much of a detrimental effect either. Feedback, when
properly applied, improves linearity, reduces distortion, and doesn't do much else. Tube preamps are sort of "easy" - I, or anyone else who knows anything abut tube design, could design a basic gain stage tube preamp, with 10 dB of feedback, or with 20 dB of feedback, and they would both sound quite nice, quite neutral, and you probably wouldn't be able to tell the difference between them. Designing one with absolutely no feedback, and still keeping the distortion very low, would be a bit trickier - but is certainly doable. (Note that I said "a basic gain stage" - otherwise known as "a line stage" - adding tone controls and other such options make it much more complicated.)
A lot of this is true because a tube preamp doesn't need output transformers, and tubes by themselves have very nice high slew rates (most of the nasty side effects possible from feedback occur when you combine too much feedback with
INSUFFICIENT slew rate.) This means that the output signal we use to apply feedback really is pretty much an inverted version of the input - like it should be. The tubes used in preamps, operated under the conditions they're likely to encounter there, also tend not to make that much distortion to begin with. In short, they sound nice without much feedback, and, if you do decide to apply feedback, it works as it should and doesn't do much harm.
Things get much more complicated with a tube
POWER AMP.
The tubes in a power amp are operating under much more trying conditions: they're being asked to supply lots of current and dissipate a lot of power. Now, we take the output from those tubes, and send it through a transformer, which adds distortion, other nonlinearities, and is a "very interesting load" in terms of impedances and phase shifts that vary with frequency, and other similar complications. And the output of that transformer has a relatively high output impedance, which means that it doesn't control the speaker very well (low damping factor), which is where you get the less well controlled bass.
Now, a quick word on what feedback
DOES, which I don't think many people understand.
Feedback takes some of the output signal, and adds it, out of phase, to the input. The math works out that, by doing this, you reduce the overall gain, but reduce the errors (the differences between the input and the output) even more. In an "op amp" this is formalized to say that the amplifier compares the input signal to the output signal, and applies its full gain to make them as close to the same as possible, which sure sounds like the formula for a "perfect amplifier". (A "theoretical op amp" has infinite gain, and would have zero distortion. Sadly, nobody makes one that's better than "close" to that.
)
So why doesn't it work with tube power amps? The problem is that, in order for feedback to work "properly", you must add/compare the output signal back to the input signal
EXACTLY OUT OF PHASE. Unfortunately, because of all the phase shift, time delays, and other "fun stuff" (mostly in the output transformer), the output signal we have
ISN'T perfectly out of phase. In fact, it's shifted in all sorts of complicated ways from what it should be. So, what we end up doing is adding the right amount of signal, but it's slightly out of whack from what it should be. Now, because of that, instead of the errors exactly cancelling out, some of them cancel out, while others end up "correcting in the wrong places"... and this correction is applied back to the input. You end up with a descending snowball effect of the imperfect corrections of errors themselves becoming new errors, which are in turn imperfectly corrected, and on and on. This is why applying feedback "around" that transformer tends to sound bad - it's not that feedback is being applied; it's that the feedback that's applied is "slightly wrong"... so there's a compromise about how much feedback to add before the benefits of having feedback are exceeded by the problems caused by its not being applied quite correctly. (This is why some tube aficionados prefer no feedback, while others prefer some; it's simply a matter of which errors annoy you more.)
(Another slight oversimplification) Tube amps with less feedback tend to have more distortion, but it's "simpler" distortion, which many people find less annoying if not downright pleasing. (Remember that adding "pure" second harmonic distortion adds fullness and "sweetness", and can actually improve intelligibility... even though technically it doesn't belong there. Most people agree that more complex "higher order" distortion sounds bad... so the tradeoff becomes one of having less of something nastier or more of something not so nasty.
My point, however, is that the effects of feedback depend on the circuit. There have been "tube op amps" that used huge amounts of feedback, and ended up having very low distortion, and sounding pretty much like good solid state amps... because their feedback was "done right". The main issue with tube
POWER amps is that, due to having to use output transformers, and the other issues that stem from having to deliver higher levels of current and power, it's basically impossible to apply feedback "correctly" to them, so you almost always end up with that tradeoff between no feedback and bad feedback.
Now, all of what I've been describing is technically referred to as "global feedback", but feedback can be applied to a single stage individually as well. In fact, many so-called "zero feedback" designs actually do apply local feedback to individual stages.
If you want more reading on that subject, you can try Googling things like: "local feedback" and "cathode degeneration" and the solid state equivalents like "emitter degeneration"
And more trivia, the cleanest buffer stage in common use, the cathode follower, actually has infinite (local) feedback.
20 DB feedback
WILL have a prominent tube sound.
Feedback takes some of the output signal, and adds it, out of phase, to the input. The math works out that, by doing this, you reduce the overall gain, but reduce the errors (the differences between the input and the output) even more. In an "op amp" this is formalized to say that the amplifier compares the input signal to the output signal, and applies its full gain to make them as close to the same as possible, which sure sounds like the formula for a "perfect amplifier". (A "theoretical op amp" has infinite gain, and would have zero distortion. Sadly, nobody makes one that's better than "close" to that. 
) 
