Titans are the crafters of worlds, the makers of Rules, the ones who set up Erfworld to be the way it is.
And what exactly has Parson been doing his whole life? Gaming. GMing. Designing games, scenarios, worlds. He was working on Gobwin Knob-ish scenario when he was summoned, for titans' sake...
I think he literally exists outside the bounds of Erfworld's rules. He's only bound by them so long as he actually is aware of them and believes in them.
After all, he comes from a world - the real world - which is governed by rules of nature, physical laws, gravity, etc. He assumes there's some sort of similar underlying fabric dictating the way Erfworld works... but Erfworld is not natural. The rules are arbitrary, chosen by the whims of its creators instead of by natural laws of science and nature.
By learning more about the rules of Erfworld, he's really sabotaging himself. When we catch him breaking a rule, like not obeying Stanley's order to manage the city, it's because he was unaware of it. Once he's aware of it, I don't think he retains that freedom.
I think he can personally break any rule he's not aware of.
I also think if he's desperate or deliberate enough he can break any rules he wants - like when he defeated the profanity filter or jumped through the Magic Portal. I don't think he's a secret caster - I think he literally can't be croaked. He's an immortal. A Titan. Essentially a god...
But he's naturally inclined to believe that a universe is a place where everybody has to follow the same set of physical rules. So since he believes that, most of the time that's what happens.
I think if he didn't know about "Move" or "Garrison Units" or "Hexes" he would have been able to walk through the hex boundary without even noticing it was there. But since he knew the rules, he felt that he should be bound by them in some way.
On the other hand, if he deliberately said "I'm going to break this rule. No Hex Boundary can contain me. I am a PLAYER!" or some other magic words signifying his willpower and urge to break the rules, he'd be able to do it.
He is literally a shaper of worlds, and can bend or break the rules as he sees fit. Perhaps he can even create new ones -- like, say, maybe uncroaking a volcano in an artificial game world that really shouldn't have any concept of "geological time" or "tectonic plates" or "dormant volcanoes."
Imagine if you will not a computer strategy game like most of the comparisons of Erfworld to our own world... but a tabletop RPG. Like Parson was going to play with his friends (other Titans, if you will). Now imagine the weird, self-contradictory idea of a character within that imaginary world -- which exists only in the minds of its players -- becoming aware of the fact that he was existing in a fake, imaginary world.
I know, it makes no sense. But somehow it kind of fits the position Parson is in - a character aware that he is a character. A PC in a world where nobody knows that they are all NPCs.
Imagine the power he would have, simply by that knowledge. Like lucid dreaming, he might have the ability to metagame, to change the "reality" he perceives to something he desires. Once you realize it's fake, you can make it do what you want -- like lucid dreaming.
The moment Parson realizes he's a Titan will be the moment he realizes Erfworld is at his mercy... and the moment the story gets boring of course. Nobody likes an omnipotent character. So it'll have to be a slow, mystery-laden reveal, with the final moment occurring near the end climax scene of the strip.