Should this 3 ply LVL bear on a single 2x4?
None of us can really answer this with confidence, not having all necessary information (or, in my case, an engineering degree). I will offer a few assumptions and suggestions based on the engineer's drawing:


A tripled, relatively squat beam is probably being used to maximize head clearance. More typically this would be a doubled 9-7/8" beam, which rests more comfortably on a single trimmer stud and fits within a 2x4 wall. You might consider whether that's a more desirable option than having a beam that exceeds the width of the current wall.
A single trimmer stud is apparently adequate for the load on the beam (though it wouldn't hurt to ask the engineer rather than us), and the attached full-height (king) stud provides the stiffness that I was concerned about in my comment above. 
On second thought, this looks like a "flush beam" situation, whereby the beam is at and above ceiling line. Concerns about beam width in relation to wall width are probably moot, and the beam will rest on doubled studs per spec. 
Otherwise, you could always double the trimmer studs to alleviate concern. This is a low-cost solution that may bring peace of mind.