Tom Brady can't solve physics equations but he can throw the football into the end zone. That's what I'm offering this corporation. I can't solve CS questions but I can deliver a great product
You say "be a programmer" to make it sound demeaning. I am not a "programmer" I am a software engineer, which is a very different way to put it. Studying CS to be a software eng is definitely not over kill.
Apt comparison, if you've ever worked in construction: platform home designs use re-usable elements that are requirements- / market-driven, with designers and structural engineers as part of the process. All architecture programs mix engineering and design / aesthetics tracks, both of which are covered on the ARE exams (loosely speaking).
Discussions regarding PE-style certification for software development often get stuck in the mud, but I'd wager that we'll see something emerge in this generation for general development (as it already exists for safety-intensive applications). And crypto may actually increase the demand for formal proofs and other deep CS concepts.
Your CS prof may have made the remark with some degree of disdain, though there are quite a few programmers / developers out there making better money than a college prof (excluding those working in private consultation).
I'd probably suggest that its like studying physics to become a plumber.
Note that I based this analogy on being a CS graduate myself and also working for a while for a chap whose academic speciality was mathematical modelling of things like water hammer.