Listing a Stack Overflow user as co-author for having provided substantial programming support

Physical presence is irrelevant. I'm a co-author of a four-author paper which came out of a Stack Exchange Q/A thread, none of whom have met in person.

What matters is intellectual contribution, and the question of whether contributing to code counts as sufficient intellectual contribution depends both on the specifics of the contribution and the field of research. I'm also a co-author of two or three psychology papers on the basis of having provided programming services, even though I would have expected an acknowledgement at most, because the culture of the lab (and probably the field more widely) where the lead author did her PhD was very generous with authorship.

The person best qualified to judge the contribution made by this SO user is you, followed by your professor. Your professor will also know the culture of your field. And if, as I presume, the professor is going to be a co-author, you would need them to agree to add another co-author. If you feel strongly about this, you should talk to your professor before you talk to the SO user about "upgrading" them. But since your professor has already given you guidance, and the third party is happy with that proposal, I suggest that you drop the issue unless you feel strongly about it.

Physical presence is not the important factor. If he's sitting at another university and you're collaborating (without Stack Overflow), you can publish together without him being present when you submit the paper. The same is true, when you collaborated via Stack Overflow in a substantial amount which justifies coauthorship.

But beware of pseudonyms. Even some "real name" here could be a pseudonym and this may be unprofessional when publishing.

On the other hand, On a paper, nobody knows you're a cat.