Then you broke the law, assuming you had a Florida license and you presented it to the Miami facility.
Florida law, Title 13 section 322.32(2), "Unlawful use of license" says "[i]t is a misdemeanor of the second degree ... for any person ... [t]o lend his or her driver's license to any other person or knowingly permit the use thereof by another."
Hmmm, I read quite a bit of difference between "retain your ID" and "permit the use of" - maybe one of us is reading something that isn't there.
Intentionally receiving a document is usually sufficient to establish possession. Some statutes say "possess", some say "use", some say use for specific purposes. If they say "possess", you're definitely potentially screwed -- if you ask for it and receive it, you possess it. If they say, "use for purposes of [x]", then you're definitely safe (since you're probably not using it for any of the prohibited purposes). If the statute just says "use", then ask a lawyer. Use is more than possession, but it's not clear exactly how much more. With luck, rational courts will hold that "use" means to use it as a means of identification and you'll be okay. This Florida statute makes it a crime to "lend" your driver's license to any other person (punishable by up to 60 days in jail). I can't imagine how permitting someone to retain something temporarily does not constitue lending, but I suppose courts might hold that unless you use it, I haven't really lent it to you. This is murky stuff, definitely not someplace you want to go without talking to a lawyer. If you possess or transfer any government-issued identify document without lawful authority in order to facilitate any violation of Federal law, 18 USC 1028(a)(7) puts you in jail for a very long time. Are you getting into that facility to facilitate breaking some obscure intellectual property or electronic privacy law?
Quite a few places "retain" your ID while you are on the premises, to include places "holding" your passport while you are there, etc, etc...
In that case, they definitely possess it, you probably lent it to them, and they may or may not be using it. Read your laws carefully. Some jurisdictions really do make it a crime to possess someone else's official identification. Receiving something intentionally usually is sufficient to establish possession. IANAL. DS