Wowww... personally I find that entirely unacceptable... to the point of being insulting. If you buy a car, even used, any reputable dealer will always provide a car with consumables that are that in good shape. Fresh oil, fresh tires, etc. Unless of course you knowingly paid for one heavily damaged tire.... and in my book, that is heavily damaged.
Sure... it might be possible to ride on them... but for how long? How long is it going to be before it blows out on you? What speed will you be travelling when that happens? Are they really so unconcerned with your safety??
Tell the dealer that it's unacceptable and that they need to fix it for you, at their cost, as they would have (and should have) done from the start. Going "halfsies" with you is just ridiculous. If the service department folks give you grief, talk to sales; if you don't make any progress, take it up with the general manager. If you still have no luck, take it up with the dealer principal and let him/her know that this is a huge breach of trust and confidence in them, and because of that, you will never ever buy a car from them again, get any service done by them, and will recommend to everyone that you know that they should avoid them ...if this isn't fixed.
Honestly, I'm just awestruck that they seem so willing to risk losing one or more long term customers over a matter of a $240 tire. That's asinine.
This just makes me realize how good I have it with my dealership. I've been their customer for over 20 years, and they have always treated me well. They don't do me any special favors or anything, but they certainly make sure that everything is done correctly, expediently, and always, always stand by their sales and their worksmanship. I've not once walked away from them feeling gypped. My worst case with them is when they couldn't duplicate a problem, but they put many hours into trying to duplicate it.