I've never used 'special' TP, but ALL toilet paper is designed to "fall apart"-- it must, or every sewer system in the country would be clogged up. I've been RV-ing and boating for many years, and I've never had a problem with TP. I've HAD a problem, twice, once in our 5th wheel, once in the houseboat. The common denominator was they were parked and hadn't moved for some time while living in them. If the 'stuff' (TP and everything else) isn't stirred up, it can't break up. TP just sitting in a jar won't dissolve, but stir it up a bit, and it should break up into a million little pieces.
1988 SkipperLiner 53x14
1995 Tracker Party Cruiser 32 *for sale*
2003 Chaparral 260 SSI
2000 Allegro Bus 40' DP