I don’t think so.
Take 3 schools’ starting COA…one relatively inexpensive for all students like Western Illinois, one middle of the road cost like Purdue, and one expensive school like Tulane. Tulane won’t care how low WIU and Purdue net COAs are, because the starting point was so much lower than Tulane’s.
Best to ask questions about how each school determined what you can pay (your sitch as an international will be different and highly variable from school to school), and how they determined what aid to give your student.
Like I said above, if there is a net COA the school can get to where your student would 100% attend, tell them that number. If a peer school offered more aid, share that. No need to have a lot of back and forth, and definitely don’t ‘argue’ (even tho I’m sure you wouldn’t I wanted to make that point for others).