Not at all surprising....
(I've never tried it with a magic eraser, which is an interesting choice, and does make perfect sense.)
(And, yes, they are exactly like using super-fine sandpaper... although their "abrasive material" is slightly softer.)
The data layer on a CD or DVD is behind a layer of clear plastic... which is the part that gets scratched.
And, if you can remove all or most of the scratches, it should again play just fine.
One thing to be careful of is exactly what you use to remove the scratches.
Depending on the angle they run in, the error correction can often tolerate one or two relative large scratches.
And, likewise, it can tolerate the surface haze left by something like a magic eraser, which is really a lot of very tiny scratches.
What you do want to avoid is a lot of "sort of fine" scratches (I wouldn't try it with a ScotchBrite pad).
You will also find that many of the "aggressive" polishes designed to remove scratches from your car's finish or headlights will also work.
I've used something called Simichrome (which is a sort of compounding polish) and it works well too.
So will "plastic scratch removers" that actually fill in small scratches with a clear sort of wax.
(As long as the LASER can "see through" the clear cover it will work just fine.)
A few things to keep in mind...
Whenever doing anything even slightly abrasive always rub from center to outside... (or outside to center)
Do NOT "go around the disc" or "rub in little circles".
Scratches that cross the actual tracks at right angles are easier to correct...
While even small scratches that follow the grooves around tend to cause errors that are more difficult to correct.
Especially with older CDs and DVDs... try to avoid wetting the disc.
So, if there's something sticky on it, try to wipe it with something damp rather than immersing it in water.
And, if you must immerse it, dry it as quickly as possible (and don't ever let it soak).
Sometimes liquids and detergents will affect the adhesive holding the layers of the disc together... and may cause it to fall apart.
Another - only somewhat related - word of warning...
Commercial CDs and DVDs have a layer of clear protective plastic on both sides...
However, CD-Rs only have a thin layer of rather delicate lacquer protecting them on the LABEL side.
Therefore, NEVER attempt to pull off a well-stuck label, or clean off something written in permanent marker, on the label side of a CD-R disc.
And, for that matter, always treat the label side carefully, and NEVER try to write on it will a ball point pen.
If the lacquer side is damaged it generally cannot be repaired.
(And, of course, avoid leaving them in the sun, since a long enough exposure to bright sunlight can eventually degrade them.)
For someone this might not be new, but wanted to share, just in case.
My wife has a set of workout DVDs she used a lot and this morning one of them kept getting stuck just a couple of minutes from the end. Video froze and audio stopped, could not even skip ahead a few seconds to resume playing.
Checked the disc and lo and behold, a couple of huge and long scratches by the edge. Used an utility I have on my Linux-based laptop and confirmed that a few sectors on the very edge of the disc were unreadable.
Plan A had been to try to make a copy of the DVD on a new disc, hoping that the optical drive in the laptop was a bit more forgiving. Being forced to scratch that plan (sorry, could not resist
) I figured that if the disc was unrecoverable I had nothing to loose trying something "extreme"... Thus, I proceeded with the attempt to remove the scratches using a Magic Eraser, the white abrasive "sponge" used for household chores. IT WORKED!! I could not believe it, as per instructions I wet one of the pads, squeezed well all of the water out of it and with just a few GENTLE passes applying moderate pressure the scratches were gone. It was like using superfine sandpaper.
I had used before the Magic Eraser for other "unconventional" jobs, like removing scuffs left by the usual guy who opens the door of his car and hit yours, leaving as a souvenir a dab of his paint, but never thought until today about using it on an optical disc.
Certainly a last resort remedy, but if the alternative is a disc that won't play, what there is to loose?