Here's how this all shook out in practice for me.

Rented from Budget at LAX using my Rapid Res number. I went inside the main building and could not see a Rapid Res or Fast Break desk. I told the clerk I had a Fast Break reservation and that I was using a new credit card that I had entered into my FB profile, and that over ther phone I had been told I would have to show the new card at the FB desk. I was told to go outside to the Fast Break area and show the credit card to the person at the exit gate.

Over the course of several Fast Break rentals at LAX, I have never seen any Budget personnel at the FB area except employees bringing additional cars to the pick-up parking slots. The screens showing FB reservation haven't worked for years and they still have computer printouts showing name and car category.

Turns out, I did not bring the new card I had entered into my FB profile and since I was running late, I told the gate agent I would just give him another card. He said he could use the one in the profile even though I did not have it with me, and I had never shown it to Budget. My rental went through to that card.

From all this, I think the whole 'need to show card" issue is a canard. I was able to use a new card I had put into my profile myself and statements by Budget phone CSRs that I would have to go the desk and show the card on my next rental were 100% wrong, in my case anyway. YMMV, but I doubt it as there is probably either a requirement or not.

Those that wrote that Budget couldn't be expected to trust the low paid gate agents with checking credit cards and other security matters might want to re-read the above. Seems they can and do.