I had a similar experience at Hilton Singapore once.

There were multiple events going on at the same time and the hotel did not have a large enough parking space to begin with. The doorman told me they were beyond full and I had to park elsewhere. When I enquired about valet, I got the same response that there's no point as they simply did not have the space.

It was out of frustration that I then said I'm a guest staying at the hotel. The doorman asked if I have the hotel key card to verify and I showed him my key card. He apologised and gestured for his valet to come over, telling me not not to worry as he'll take care of things. I did still giving them a little tip in appreciation. Interestingly I wasn't charged for valet services during checkout.