How does Publishers Clearing House get by with illegal advertising?

They don't. I'm not sure what you think is "illegal advertising". The letters that I'm aware of say "you MAY have already won", which is true, and PCH does not require that you actually subscribe to anything to claim a prize (if you're not bright enough to read what they send carefully enough to discover this, then it's hardly PCH's fault).

They do make it easy for you to think that you've won, and they do make it easy for you to subscribe, but that's why it's called advertising as opposed to "let's give a bunch of free money away."