How serious should I regard the "compliments" in an email denying my application?
I would take it as simply a polite way to decline your application.  They no doubt really do get a lot of strong applications (every decent program does), and in many cultures such as the US there is a tendency to "sugar-coat" bad news with compliments (I don't know if your application was in the US, but I believe this practice turns up elsewhere as well).  You would actually probably get less praise if you got in---after all, the acceptance is compliment enough.