The US Coast Guard would do the same thing. Was the boat in danger of
sinking or hitting a rock or was some in a medical emergency, then they
would go after you. I guess falling off your boat drunk qualifies.

Falling off the boat, drunk or sober, will always qualify as an emergency until
the MOB is recovered.

And you are right, the USCG will offer to call a commercial tow service unless
you claim there is imminent risk to persons or property. Getting sea sick in
5-footers isn't the sort of risk they'll send out a helicopter to resolve. :-)