That's exactly why you don't define it like "Line of Sight." If it meant Line of Sight, it'd say Line of Sight. I mean, I feel like you've answered your own question: if it really were Line of Sight, two of the portals would never actually activate; therefore, the only logical solution is that it is not reliant on Line of Sight. Right?
The different missions are designed to be used SOLELY with the specific type of Threat card listed on the setup page. The missions do not work correctly if you change those up. But, that said, if you don't want to use the Invasion Threat card, you can opt to play one of the missions that uses a different Threat type.
But dude, I'm positive about this. It's not line of sight. The card's not even ambiguously worded. They specifically chose the words "continuous path" because it means something different than "line of sight". A Marine does not have Line of Sight around corners, for instance, but a Marine can walk (using a "Continuous Path" of squares) around corners.
Continuous path and Line of sight are totally different. Continuous path is where the Marine can step if he had infinite speed but without opening doors. You can step around a corner but you cannot see around it. Practically, the Marine opening the door can step anywhere in that room now, so all portals in there are flipped.
Also you don't get to choose your Threat Card to use (unlike Event and Invasion) so sadly you are stuck with it...