Pretty sure it's NOT possible in any version of this game.

Nope, not in this game.

I came across this:

https://strategywiki.org/wiki/Disgaea_2:_Cursed_Memories/Hospital_prizes

"Note that the hospital DOES give out legendary items. They are very rare to show up on the list though. "

Which says that you can get Legendaries, but maybe it was for an older version of the game?

*shrugs*
If I were to take a wager, the person who wrote that part made some sort of mistake, like misremembering from another game or mistaking what they saw and assuming it was possible. Even if it is/was possible, it's not really worth your time.

Yes, you can get legendaries from hospital rewards in this version of the game. It takes a whole load of backing in and out of the menu to reroll the rewards, so it generally isn't worth the time.