Specifically, I’m referring to a situation in which you’re not a guest of the hotel in question, but you’re on foot, and suddenly need a taxi. In my particular case, there were problems with the subway and the trains were stopping several stations away from where I needed to be. I was already late for my appointment, so I hustled up the stairs to the street. I needed a taxi. Where to get one in downtown L.A.? The most obvious and convenient spot was one of the big hotels, which was only a block away. So I went over there and walked up to the first in line and asked if he was available. He was, so I got in and off we went.
Was that a faux pas? Should I have gone to the doorman and asked him to flag one for me, and given him a fin for his trouble?
The doorman and taxi-stand is there as a service to paying guests. If you were not a guest but needed the service, you should have requested it of the doorman and tipped him appropriately.
Just my opinion and it comes from a guy who can’t run into a McDonald’s to “just use the restroom” without at least buying a small drink so I don’t feel I used their service without making a purchase. 
On further reflection, I disagree. The taxis are licensed by the city to serve the public. If a half dozen cabs are standing idle in front of a hotel, and there’s no special rush of guests wanting one, I can’t see the harm. At least in a city like L.A. where we don’t have public taxi stands.
Then I misunderstood your post. I thought you meant that the taxis, although licensed by the city to serve the public, were a gathered at the hotel’s taxi stand. Thereby, the collection point being the taxi stand is provided by the hotel and thus if you used it, you should tip.
If they taxis were just standing idle in front of a hotel, as your 2nd post describes, then no - you need not tip for the service as none was truly provided.
I’d akin it to the same situation in NYC. I can hail a taxi from the street almost anywhere. If, however, I walk by the Waldorf-Astoria and have the doorman or bell-staff hail the taxi I owe them a tip.
MeanJoe
No, you got it right the first time. The taxis were definitely inside the hotel’s pick-up/drop-off area, and not on the street. But they’re still public conveyances, IMHO.
Obviously though, as I said, I would give way to a rush of hotel guests needing taxis