Since you raised your doubts, I just re-watched it - series 3, episode 4. And I confirm the view.
The whole episode is about the clumsiness of living, consistently with the project idea ("the IT crowd", outcast specialists with little interface to the public, which is a mass of people thrown into some role "«not doing much work but constantly having affairs»" - confused humans -, with a link which is the portrait of incompetence trying to make a living - trying to live - into something she does not understand). All the characters do is "attempting", trying to fit a role. The difficulties of living roles could be a trigger for the development of the substory involving Douglas Reynholm and April (and the gender instrumental to that). The whole idea climaxes in the "collapse of civilization" when the "stakeholders", as "topmost layer of the role-players", are in front of the catastrophic loss of the Internet, and the "punchline from above" is that of Moss: «It really isn't that funny» - of course, because it is tragic.
While I could see that the "It's over" scene could be to some extent insensitive, given that the writers may have supposed that it would be something lived by a number in such group, it was instrumental to the fight scene, which is a consolidated topos. And the "victory" seems to be on the other side, since the "punchline from inside" is that of Douglas, which ends the episode crying, going "It's not the same!" (It's not the same without her, or him - as she was both the "other half" and the "pal"). So, not only I do not see a phobia, but on the contrary, I see the opposite message, towards seeing people for what they are, and to love that whatever they are (also since the premise of the whole is, as said, that they will be confused imperfect players) - Douglas could not and he is alone crying.