The '86 Celtics are the prime example of a team that could have done it, but fits the "didn't care about the regular season" argument:
1. They lost one game at home the entire season, including playoffs (56-1 overall). They'd go on road trips and just mess around a couple games at a time (for instance, Bird used to play with his off hand because he'd get so bored). They had multiple two game losing streaks because they just didn't try. They just knew they weren't losing at home. Plain and simple. So if they got home court, it wouldn't matter what their record was.
1A. By that same token, Steve Kerr said this about the '96 Bulls: there are a number of back-to-backs, especially on the road, where even good teams just pack it in for the second game, and it amounts to a handful of extra/avoidable/bad losses per season. Teams like the '86 Celtics didn't care about those games. But Jordan was so competitive that he was responsible for winning those extra games. Without Jordan caring as much, that Bulls were probably a 65 to 67 win team, just like everyone other great team.
2. The '96 Bulls had the fortune of playing at a time when the league was at its most diluted point (they won 72 games with Wennington and Longley as their centers!). The Raptors and Grizzlies were added that season, so there's six games that were basically gimmes for a team like the Bulls. Six teams had been added in eight years, and the talent pool hadn't caught up yet, especially with two brand new teams. I could also dive into lazy players and bloated contracts, but it's too easy.
2A. Remember, the '86 Celtics, even while goofing around, managed 67 wins when the league was at its highest concentration of talent. Mass expansion set in two seasons later.