I think the argument is that it's a space that is accessible by everyone without any sort of gatekeeping, that makes it a public space. Whereas a forum such as somethingawful would be considered more private as there is a subscription fee for membership.
To me the issue isn't the lack of literal gatekeeping, its the intended audience. If I'm having a conversation in public with my friends, I still have a reasonable expectation that my conversation is "private" as long as I make an effort to keep it among those in my group. That someone could walk by, eavesdrop and overhear something objectionable doesn't meaningfully alter this dynamic. I see subreddits as similar to this. The fact that there is a specific URL that indicates its topic is enough gatekeeping to warrant the conversations as "private", in terms of who is the expected target of the conversation. In the case of fatpeoplehate, the insulation of the content of the sub makes it reasonable to expect that consumers of the content will be "in on the joke". Objecting to the content because its in a "public space" and therefore not appropriate for public consumption doesn't make sense.
