That's likely because restaurants have exclusivity deals with either supplier to get a discount - Coke gets you Coke, Sprite and Fanta, Pepsi gets you Mirinda, Pepsi and 7up. It's not the restaurant blocking you with fake advertising, but just stating that they simply don't have it.

Now if they were getting supplied by both, then asking the same, that would be a better analogy.

If they have both, in some places, you're likely to be asked "What kind of coke?" to which "Pepsi," is an acceptable answer.

That’s only due to a regionalism where ‘coke’ means fizzy drink, soda pop, etc. not because of sales incentives.

Right, which makes it a genericized trademark.