From a “can the truck tow it safely mechanically” standpoint, you’re correct. The 250 Tremor is identical to the 350 Tremor assuming the same engine for each.
From purely a ”getting scaled on the side of the road standpoint” all that matters is that your vehicle (both truck and trailer) is licensed for their weight. If you’re over your licensed weight, you can be ticketed.
I know for a fact that in WA licensed weight is completely independent of GVWR/GCWR, and it’s likely this way in most, if not all, states (contact your DOL to confirm, of course

). For example, my F-150 is licensed for 8000 pounds even though it has a GVWR of 7200. I could license it for 11,300 and match a 350 if I wanted, and would just need to pay the additional registration fees.
Where this gets fuzzy is from a liability and general “dangerous driving” standpoint. While I haven’t heard of any specific stories in this regard, it’s not hard to imagine. From what I’ve read, DOT officers care a lot about GAWR and tire load ratings but not really GVWR. If you are over either of those, I bet there’s
something they can ticket you for if they want to, basically falling under negligence or dangerous driving.
Additionally, if you get into an accident and are over GVWR/GCWR/GAWR/tire ratings, it certainly seems possible that not only would you be susceptible to the same tickets mentioned above, but it seems quite possible your insurance company could use that information to deny coverage.
Again, I haven’t specifically heard of that happening. But it’s contract law so it seems within the realm of possibility, even if the truck is technically derated and just as mechanically capable as a 350.
Ironically, with the 250, because of the smaller GVWR, you can tow a larger GVWR trailer before hitting the 26,001 pound magic number that requires you to get a CDL (with the exception of RVs - though in some states an RV endorsement is required instead). But if you’re pushing it that high, then you start to run into the other concerns above, of course.