That undersells it. The data on hybrid drivetrains is pretty clear--it's definitely more reliable. Even mechanics will tell you that; certainly mine did, and he's not a masochist. Start+stop is hell on mechanical drivetrains. It's a no-brainer when purchasing a new car except that there's still a premium for hybrid, so the RoI might not be there given baseline reliability and depending on your preferences. Though the premium gap is closing, at least for non-plugin hybrids. Plugin hybrids are the new premium option in model lineups, so traditional hybrids are moving down market.
My plugin hybrid (I just bought it 2 weeks ago) is on track to save me $200/month over the others similar vehicle it replaced (minivan with the same engine, but 10 years difference in years, so lots of other differences).
At least for Toyota hybrids, the intuition is that the traditional ICE transmission system is replaced by what Toyota calls a "power split device" which continuously feeds and balances the electric and combustion power sources. This power split device uses a simpler gearing system (enabled by the high torque electric motors) and appears to be mechanically simpler and more reliable than traditional transmission systems (which probably wear out quicker than the engine in most ICEs).