I personally think there are two different questions.
Question one is; Can the water in X container be kept clean enough? Can someone keep a 1/2 gallon clean enough? Can you keep a QT cup clean enough? I bet you can. It takes dedication, but you can keep water clean enough.
Question two is; Is it big enough for the fish to express natural activities? I see a lot of smaller tanks and for me the answer is generally no. 1 gallons are usually built tall for a small footprint... the fish can't swim it's length twice over the long way, and only has space to comfortable turn around width wise. To me, this isn't an appropriate tank. For me, when I look at tank side... I think a fish needs a space where it can swim horizontally at least 3-4 times it's own body length... and at least two on the short side. Nearly every small tank I see fails to accomplish this.
Anyway, I had another more ranty thread up, but it got locked so, that's all I'm gonna say here on the matter. Clean water =/= living space imo. You could keep 1 dry measuring cup worth of water clean enough for a fish but it wouldn't be an appropriate home.