They can. I am doing daily water changes to keep the water as clean as possible for healing. I have givin him a daily salt bath, and I am treating his fin injuries with Bettafix (this helped my other betta in no time) and I have slightly raised the temperature of the tank to 26C. I have not started treating him with any type of Ich medication. He is eating, not spitting it out. I have also lowered the level of the water so he doesnt use to much energy going up for air. He hasn't moved around much, just kinda lays on top of his leaf. I sprinkle the food above him so he doesn't have to move to get it.I once had a betta in my community tank. One of the other members of my tank was a Paradise Fish. What I learned is that apparently Paradise Fish and Bettas don't get along either. The Paradise Fish shredded the betta. His fins were completely chewed off. I removed the Betta to another tank and he recovered with no problem. I don't remember if I used aquarium salt in the tank to reduce infection or not. Might want to check if Bettas can tolerate salt. But he was back to normal in no time.
My other Betta, the one he got into the little fight with, is in my 40g tank with my platys. He is swimming happily, blowing bubbles at my other fish. I do not have any fish in that community that are known to be aggresive with bettas.