Can A Doctor Legally Detain A Patient Who Can't Produce A Urine Sample?

My urologist is a crotchety old man, hard of hearing and often loud and rude. Unfortunately I live in a small town in NE Florida and he's the only urologist within 35 miles. A month ago, he collected a urine sample, told me he thought "something was growing in it", put me on an antibiotic and then sent me to Quest for a urinalysis. So I complied, but Quest failed to send him the test results. I downloaded the results off Quest's web site, printed it out and took it to the followup appointment this morning, since his office called me yesterday and said they had not received the results from Quest. Gave the printout to one of the staff who said she would enter it into my record and then return the printout.

When the doctor came in to the exam room, he wanted to know why I didn't give another urine sample this time. I explained that the test results said "no growth detected", that I took all the antibiotics anyway, and that I had two cups of coffee earlier and had emptied my bladder before leaving home, not expecting to have to give another sample. I guess he thought I was lying, as he then told me he would "lock the door and stop me from leaving until I produced a urine sample". I was a bit stunned at his temerity and his thinking I was lying, needless to say. Luckily the staffer came in and gave him the test result printout, so he said everything was OK and that he would see me again in 6 months. I won't be going back, of course, despite having to find another urologist somewhere else.

So my question is, could he have legally detained me, or would that have constituted false arrest?