I think this is basically true in moderation.
I certainly agree that a lot of problems (including a lot of very difficult problems!) are not amenable to purely technical solutions.
But sometimes you have a difficult, technical bug to fix, and the "people problem" is making sure that someone has the knowledge, context, time, and incentive to fix it. This is not necessarily easy!
... especially if enough people have bought into "everything is a people problem", because then the technical work of fixing the bugs isn't valued or incentivized. Why would it be? It's not solving a people problem.
I think the viewpoint "everything is a people problem" can create a feedback loop that leads to poor incentives - which, ironically, is a people problem.