To play devil's advocate here:
Cross-dimensional hopping isn't anything new in the roleplayer circles in MMO's. I knew people that brought characters from other games, from other genres, and even porting their characters from their pen-n-paper tales with their entire histories intact, regardless of how they meshed with this new world. The problem with this is that, for roleplaying- collaborative storytelling- to work, we have to have some mutual agreement on many story elements- one being the lore that ties this world together. Many cross-dimension hoppers bring in too much from their "old world" to the new one, creating discomfort for the people that are trying to work within that world's lore.
Now, there's different degrees of lore-complience. You can be directly tied to the lore, compliant by slopping through the "unspoken" parts of the lore, and then there's the lore-defiant that actively ignore the lore. You can have a lore-compliant story that's doesn't tie into the lore- it just doesn't go overtly AGAINST the lore, either. A lore-defiant character is one that expressly tries to insert elements that are contradicted by the lore. Where you draw the line varies with each individual player, but I draw the line on where it starts to interfere with others' stories.
Most roleplayers have to do some form of selective editing of their character histories, to some degree. I don't pretend that Chase Arcanum Arrested Countess Crey a dozen times, just because I played that arc multiple times, but I may incorporate parts of that tale into his "official" story. Likewise, when I roleplay, some of my interactions with other characters need to be edited out because... well... they're too far out there for me to WANT them to be part of the story.
I once suffered through a RP session in SWG where a new visitor tried to reveal that she wasn't a blue Twi'lek, but a blue dragon, transforming in front of us, from what was essentially the realm of dragonlance. Her argument in support of this was that there were millions of galaxies out there, so who's to say that one of them wasn't the Dragonlance world. SWG was essentially sci-fantasy after all. It was so far outside the norm of the lore, though, that I think everyone else was justified in tuning her out when she persisted. They made an honest effort for too long, derailing their own fun to try to appease the dragon, but at the cost of their own narrative.
I recall a different debate in EQ2, where someone wanted to RP a vampire, but not as the EQ lore used vampirism... theirs was somewhere between Anne Rice and Twilight. Again, people tried to work with her, but she was upset that every time she'd explain she was a vampire, people would assume the official lore vampy and she'd have to explain she was different... and all that time explaining took time away from the story she wanted to progress. she expected everyone to ignore their own understanding of the lore and our own experiences tied to vampiric lore and just accept her own.
You're right that the CoH lore, with Portal Corps, would allow interdimensional travel.
The question would be whether the CO lore allows it (I believe it does) because THAT'S the lore that other people are using with their own characters. If it does allow portal-hopping, is it safe to admit to being one? what's the legal status of these people (are they seen as illegal invaders, treated suspiciously, or embraced warmly?) It could be that her characters shouldn't be so open about the specifics of her origin (for that matter, what if someone used her information to travel BACK to Paragon.... maybe she should be more secretive to help protect her homeworld).
I can't see the specifics mentioned here being an issue in the CO world-- the pen n paper game that this was based on was well-crafted to allow myriad backstories, even ones that seem conflicting. I suspect this is something else- simple tribalism. CoH was a rival for very long- and more successful than CO in population, appeal, and developer activity. The forums there show a mix of acceptance and contempt to CoH, and that may have colored these peoples' sentiments to your chosen story.