I know most of us don't run one, myself included, most of the time...
but they all should really have an air filter of some sort, if we want
to wring maximum life out of them.

All it takes is a single piece of grit, to do the damage you described. (The scratched Cyl)

Did the engine have a broken bearing too?
Or is that just something you thought may have caused the scratch?

If everything else is intact, they're probably right about debris coming into carb.
If something else internal is fubar, then I'd have my doubts.
(Though it's still possible that excessive dirt entry could have
destroyed the bearings, too. Especially in a two cycle engine)

I know folks who will say they've been doing it sans filter for forever,
with no problems at all... but let the right piece of grit get sucked in,
just one time, and BAM.