I don't like the product placement either but I don't understand how it doesn't make sense. The US doesn't exist in the XV world so it can be assumed that Coleman was independently founded and named by another fantasy citizen of a fantasy nation and it just so happens to resemble it's real life counterpart. I don't think it's too far removed from accepting XV's use of the Latin alphabet, the Gregorian calender, Latin and Arabic numerals, and the English and Japanese languages. They exist unaccompanied by their nation of origin so why can't Coleman?
I can buy why people don't like how something is advertised, but I really don't understand how having Coleman is simply inexcusable or impossible in that world after all the things you've listed. I completely agree.