I only have limited experience with AA and pets, but I might as well share --- When I moved to/from Hawaii with my two cats, the carriers I thought may be too small considering AA's wording. Similar to what you said, they can move around, stand, but there wasn't really a ton of space. AA did a quick visual check, but didn't pull a tape measure or ask the cats to do turnaround. (Note, the cats were transported as cargo a day before my flights, not at a check in desk -- note that Hawaii's laws make transporting pets a very involved process, and we had to follow all sorts of weather rules/routing rules to ensure the cats wouldn't die in the heat on a tarmac somewhere). From what I have noticed, dogs in the cabin are usually in very small carriers as well.

If the dog isn't constricted (i.e. it can move around) like you say, and you are making an honest attempt at obeying the rules and paying the fees, I doubt you will run into issues.