Happened to me over 10 years ago - rejection letter had this extra sentence at the end: "In addition, I really love your cover letter". The company back then had about 1000 employees, but it was for a position in a remote office which was probably very small.
Regarding "are they stupid enough to actually believe it" - I don't know, but what do people usually write in cover letters? When I wrote it - it was basically CV, just in text form instead of bullet points. But then _lying_ in cover letter is basically the same as lying on CV, no? Or, if companies tend to believe CVs, I would expect them to at least _pretend_ to believe cover letters, too.
Regarding "are they stupid enough to actually believe it" - I don't know, but what do people usually write in cover letters? When I wrote it - it was basically CV, just in text form instead of bullet points. But then _lying_ in cover letter is basically the same as lying on CV, no? Or, if companies tend to believe CVs, I would expect them to at least _pretend_ to believe cover letters, too.