Good on you for having the meta-cognition to recognize it.
I've graded many exams in my university days (and set some myself), and it's exceedingly obvious that that's what many students are doing. I do wonder though how often they manage to fly under the radar. I'm sure it happens, as you described.
(This is also the reason why I strongly believe that in exams where students write free-form answers, points should be subtracted for incorrect statements even if a correct solution is somewhere in the word salad.)