There is a fair chance of that, actually. If you start enumerating the ones that are obvious even to lay people (one rocket, one satellite, one set of mirrors and so on) then this is probably an extremely impressive low number.
I've been binging JWST content and definitely recall John Mayer saying in at least one interview that 344 single points of failure was as low as they could get it. And I can believe it. If you watch some of the more detailed interviews, he always stresses how every design choice was heavily labored over and reviewed.
It's an absolutely amazing effort, from the design through all of the problems they had to deal with along the way to seeing it sit there on top of that booster. A few months from now we could be in a completely new era of astronomy.
