And you think BA's opinion on modular vs integrated really matters? I don't believe for a moment it does. The chances of BA offering anyone their first job are so remote it doesn't bear consideration.
however we have to remember some companies dont like to change their ways. (old school, most schools)
What do you base this gem on exactly? It sounds to me like you have your own reasons for choosing your route. So stick with them and give it a rest.