Billy Joel realises that comparing a brief spell in a luxury clinic getting treated for drinking too much with being shipped off to a Nazi death camp might be a bit much:
Briefly, he realised it was a facile and offensive comparison. But then decided to go with it anyway.
Yes, that does sound a lot like being separated from your family, starved, getting experimented upon, being shuffled into a room and getting slowly gassed to death. Presumably someone removed Joel's sense of perspective with a pair of pliers.