My "theory" aligns with this and is based on how it all unfolds at the end of the film and a couple of key moments.
I believed that Teddy was who he believed that he was, and that they were trying to convince him that he was someone else. They were taking advantage of his troubled past and his PTSD to engineer a situation where he could take the blame for something he didn't do. If that makes sense.
"This places makes me wonder, which would be worse; to live as a monster, or die as a good man."
...Said at the end, before he walked off to his death. I took that line as Teddy's acceptance that there was no way of proving that he wasn't a monster while he was there, and, as he now had no way of getting of the island; the alternative is to "die as a good man" (the man he actually is, the man that they also know he actually is but are also acting like they are pretending he is to later say they were acting - because they want to be able to portray him to the rest of the world as someone he isn't). If that makes sense.
Teddy sees the orderlies walking over with the medication and he understands what is going on and that, he knows that if he continues to insist that he is an officer named Teddy Daniels (which he actually is), then they are going to kill him because their experiment has failed and they haven't been able to convince him otherwise (in the lighthouse scene, Chuck says something like "if we fail with you, then everything that we've been working on here will all be discredited", so you can see the importance of trying to get him to admit to being that "monster"). But, he's not going to admit to it because it's not true, yet he sees no way out of his current situation and does not want to assume the role of the monstrous character that they created for him, so he opts to play along with their ruse and acts as if none of the stuff in the lighthouse happened, and acts as if he doesn't know that the guy next to him really wasn't his partner, "Chuck".
It's not just that line that convinced me of this though, it's more the knowing look that he gives Chuck after the line and Chuck's reaction to it, and the long pause that he takes before making that look. After delivering that line and walking off, it takes Chuck by surprise that this man is willing to just accept his death rather than admit he is someone he is not. As Teddy walks off to his death, Chuck is looking at him as if he can't believe what he's doing, and drops character just for that second and he calls after him by his real name, "Teddy?". However (and this is why it's so brilliantly written), of course, just before that, if you watch that clip from the start you'll remember that Chuck had been engaging with Teddy as if he were his partner, so he would have been calling him Teddy anyway in that moment. But, I believe in that very subtle change of tone from Ruffalo and I think that is what helps tell the truth to the audience. However, because of how it's setup in that moment, there's no real definitive answer as to whether that was an admission of the truth by Chuck or not.