Does a recent crown placement cause an adjacent tooth to crack/break off?

The crown placement would not likely cause the adjacent tooth to have problems.If you had a large existing filling on the tooth, it is possible there is just a coincidence. Fillings act like a 'wedge' inside of a tooth and can lead to fracture. If it was a 'perfect' tooth with no filling, or other work done to it I'd go back to the dentist. It is possible there are other things going on, like bruxism or habit that is causing increase wear and tear on your teeth.

While dentists do their best to see/diagnose everything, some issues are not obvious.  It does not mean negligence, it simply means data wasn't present at some point. Most cracks/fractures do not show on xrays, and unless light hits a tooth in "just" the right way, we often cannot see them.  If there are no symptoms, we will miss them, especially if "we have bigger fish to fry."New crowns/restorations can exert pressure to adjacent teeth, but not in clinically significant amounts.  If other teeth start to have issues around the same time as new dental work, it most often is simply a factor of pre-existing but undiagnosed issues.  It is the whole "causation vs correlation" debate.I would get the teeth fixed, but I would not suggest blame to anyone.