For the area of the ambulance service I work for we tend not to smash windows or kick in doors. If we have an access issue we use the fire service who are now very adept at drilling locks with minimal damage, and who then replace the lock cylinder and leave replacement keys.
I don't know who pays for that in all honesty.
Obviously if I felt it was a life or death situation, I'd be forcing entry rather than wait the 10-15 minutes the fire service take to attend, but very few calls are actually life or death, contrary to popular belief.
I did have an access problem this morning where the keysafe number I'd been given for the property was incorrect. In this case it was faster for me to work through a list of logical guesses for the number using information I knew about the patient and I'd gained access within a few minutes (not the obvious number).
There would be little point asking the crew where the call originated from, we just get given the job as is, with no access to background data.