A heater is a must especially if your area gets chilly. Filter isn't necessary as long as you're up to the cleanings.. If you think that he can handle a 1 gallon and you can as well. Then let him be. Its upto you. :)
Ofl is just trying to explain what kind of scenario one should have a betta in, how one should let the betta get used to moving into a bigger tank etc..
My male bettas are in 2.5-3 gallon tanks with nothing except for a few plastic plants to rest on , caves to hide in and a heater in the colder months. I clean out their water 2 times a week and they're doing great. :) That's how I do it. What you do can be completely different as long as it suits your and the betta's needs.