AES has a back door of sorts. AES was chosen over, say, Blowfish because AES is easier to implement in IoT (wasn't called that back then, but that is the idea). This is public knowledge.
Well, NSA has its own fabs and can make billions of AES decryptors, so you know the routine.
You don't need an idiot Filiol backdoor, just one that the NSA can use. In BEA-1 case, once you know the backdoor, for all intents and purposes the algorithm is broken; the break is simply too easy to implement.
The main problem with Filiol et al premise is that they want a COMMON backdoor that is "easy" to use. This is logically equivalent to a promiscuous key-- once known, game over. There is no magic backdoor method in mathematics that is going to let Joe Plod read encrypted data easily yet prevents Jane Cracker from doing the same once the secret is out.