true or false? I heard that after you've sync'd the new set with the car, every time you swap tire sets all you need to do is deflate the replacement tires and reinflate them and the tpms will register correctly.
/anecdotal evidence/Thats how it worked for me, Got a carriage bolt in my passenger side rear. left my wheel at the tire shop to get a replacement and when i got it back still had the warning. put it up on the jack and let the air out of the tire/re-inflated it to spec and drove about 2 miles before the sensor reset.
worst case you can drive by most independent tire shops and they'll take care of it for free, I usually grab them a starbucks to say thanks : )