I think they put what they can get as long as it meets the spec, its not by trim level that I can tell (they seem to change randomly over time though they started with Bridgestone).
I have heard elsewhere that the version of tires OEM for a car tend be different then stock similar brand/model. For what it is worth the two sizes on Palisade and
Telluride have different feel and handling characteristics. 245/60/18 versus 245/50/20 (20 percent more rubber and air) on 60/18s. Consumer Reports actually dinged Palisade for 20s even though both cars come in both sizes (they and some others feel the 18 feel and
handle better). CR Mainly because there tester
Telluride was an EX which is basically like an SEL Premium with Drivers came on 18s. Kind of silly though both base models come on 18s.
Telluride Jumps to 20s on the SEL equivlant S, Jumps back to 18s as noted on EX and then back to 20s on SX. Palisade 18s on base SE/SEL and then Jumps to 20s Convenience package all the way though limited. Then you have people go crazy and buy even larger wheels up to 22s with really low profiles to fit.
Anyway back to tires... When you buying you can make that part of your purchase decision if you wish. I was and am fine with Bridgestone. When I need new "sneakers" I'll buy the best rated for the price at the time. Maybe get All Weather instead of All Season. Time will tell. Personally there are few things on cars that are consumables and as long as they last loosely as long as they should I'm fine replacing them: Tires, Batteries (around 35K-50K). Wipers around once a season or two.
For what it worth Stock tires on my 2005 Odyssey were Michelin Energy, Lasted only around 30K and handled pretty decent but not "great". Replacements were much better (Yokohama and later different Michelin). Choices became greater over time too.