Yeah, a better comparison would be if you go to the store intending to buy Coke, but at the front of the soda aisle is a giant display with Pepsi on sale -- so you end up buying Pepsi. Which, come to think of it, happens to me all the time.

Ok a better representation would be I ask a clerk for a Coke but I get handed a Pepsi and I have to say, no, I asked for a Coke, not a Pepsi. But depending on how much Pepsi paid them I may get the Pepsi handed to me several times till I get the Coke (sometimes some trademarked brands are way down -maybe below the fold.)

At a lot of restaurants, I ask for a Coke and I'm told "Would Pepsi be OK?"

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.