I think its more so along the lines of always having a car in the shop. I'd be unhappy with my car regardless of miles if I had to take it into the shop often.
As for the OP question.
If your car is within warranty and X problem happens, the only way they can deny the warranty work is if they can prove whatever you did or didn't do caused the damage. For example, if they find that the engine shows signs of low oil, or too high of oil, or if they find signs of really old oil, they could argue that the failure was caused by that. Running the wrong weight oil could also be an issue if they could prove that because of the wrong weight oil, the car threw a rod. Good luck with that...
Problem is, dealerships would rather you pay them for a new motor than to get paid the warranty rate by the company that made the car. Subaru guys will know what I'm talking about with STI motors blowing up and some dealerships doing anything they can to deny the work even on cars with less than 10K miles...
Some nissan dealerships did the same with the 350Z and the oil burners as with the first year 350Z transmissions which almost all of them had to be replaced.
Know your rights and you'll you wont have an issue.
Personal story of dealerships trying to get warranty work paid for out of pocket by me.
We had a 2007 Civic SI, it had the normal 3rd gear issue which pretty much all SIs of that year had. I called 3 different Honda dealerships and each one said the same thing.
We would be more than happy to replace the 3rd gear in your transmission, the job is $2800 when can we schedule the appointment? I then questioned why it wasnt covered under warranty and was told sorry your bumper to bumper warranty is up, rather then give them my warranty work, I figured, [censored], the next Honda dealership will want the job... nope 2nd dealership didn't want it either! finally on the 3rd dealership when they told me it wasn't covered under the bumper to bumper warranty I told the guy to cut the [censored] and explain to me why my transmission WAS NOT covered under the drivetrain warranty which the car was still under, and why they kept saying it was only covered under the bumper to bumper warranty, the guy got defensive and said well sir, we would be more than happy to talk with Honda of American on your behalf to see if they would extend the transmission to be apart of the drive train warranty. I told the guy that's ok, I'll personally call them and ask why it wasn't covered under the drivetrain warranty when the transmission is apart of the drivetrain. Guy replied, sir, i'll order the parts today and will call you when they come in.