I think the OP is being overly cranky.
First, I don't see the comment "all this back and forth over the interwebz is driving me crazy" as snarky or angry at all. It's just a statement of fact, along the same lines as "let's sit down to have this conversation, my feet are killing me."
It was perfectly reasonable for the OP to ask the houseguest if he wanted to extend his stay and petsit, and it was perfectly reasonable to offer to pay his train ticket change. After all, it could have turned out that he would have LOVED to petsit if not for the cost of changing his ticket. Perhaps like many of us, he just didn't know how to say no. The OP could have worded it better perhaps, ie "Well if I paid for your ticket change, would you want to, or should I ask someone else?" That would have given him the opportunity to say, "I think you'd better get someone else; I have to be back in HomeCity anyway."
I don't know if I'd have been particularly offended by his making other suggestions even if they were no good. I don't know exactly how that conversation went down, but is it possible he started offering these other suggestions as a result of feeling pressured by the OP to find a solution?
As for having the other person pick him up, perhaps he felt he was saving the OP a trip and she'd be relieved. After all, she was going to pick him up, take him back to her place, and go do something else. Maybe he thought she'd like to be invited for breakfast; fine if she couldn't make it, but it's nice to be invited! It does sound as though he didn't think the key issue through though. I agree with the previous suggestion that a good response would be, "I can't make it out for breakfast as I have prior plans, so if you can get here before X time to get a key, great, but if not, you'll have to wait till I get home and make your own way here."
I do think that he should never presume to be able to invite some unknown (to the OP) friend inside though, whether she is home or not, but especially if she isn't home.