Yes, the White splash goes a long way towards helping defeat combo. Containment Priest comes in against some of the most difficult problems for this deck: Sneak and Show, Dredge, GSZ/Natural Order, Reanimator, Aether Vial... The fact that it is cascade-able *and* functions as a clock makes it even better.
The way I see it, the Lejay approach to building the deck is correct: the maindeck is constructed to beat every 'fair' strategy pre-side, and the sideboard goes a bit overboard with dealing with combo via Meddling Mage, targeted Discard, Containment Priest, and various bomb singletons (e.g.
Null Rod) to win games 2 and 3. Sometimes you can steal game 1 here and there against combo due to them fizzling and/or a timely FoW + Liliana or whatever.
Regarding the current format: Rest in Peace is at an all-time low right now due to people wanting to abuse Treasure Cruise, making BUG strategies better than they formerly were. While I think Ancestral Visions is the better card for this deck over Treasure Cruise, 1-2
Dig Through Time are a possibility here. Popular token-generating creatures like Young Pyromancer and the soon-to-be-released
Monastery Mentor aren't too problematic as Black has plenty of ways with dealing with X/1 creatures: Toxic Deluge, Golgari Charm, and various Enchantments (e.g.
Night of Souls' Betrayal,
Illness in the Ranks,
Engineered Plague, etc.). Sure, Liliana isn't quite the bomb she used to be, but she's still fantastic against UW(r) Miracles and certain Delver strategies which remain popular.
The reason BUG hasn't been as popular is likely due to the common perception that other decks can slot in 4 TCruise and have virtually the same sort of card advantage without having to play clunky cards like Shardless Agent and Ancestral Visions. The flaw in this view is that playing a lot of filler cards like Gitaxian Probe to fuel TC and refill your hand isn't necessarily as powerful as working towards the endgame board-state that BUG permits. Drawing 3 cards is powerful, but not that amazing if you're only getting more cantrips or Daze in the late-game.