I'll get back into the general topic and leave the details of the Caldari situation to those of you that know it better.
As far as I go both IC and OOCly, claiming you only support your faction by being a member of the FW side of it is both limiting RP and gameplay, and foolish. First, what happens to those factions that don't have FW? Can I be loyal to Sansha, if there is no war theater for it? You can even go beyond, what happens to those factions that lack military commitment? Can I be supportive of the Servant Sisters if I kill in a war theater? Sure, some may say, the Sisters have quite a dark side, but is that their only side?
As for factions that do have war theaters, do they only participate in war? The answer is no. I created a corporation, the OQ, that defended the Empire from its internal enemy. We did get into FW, but we existed way before, and even after we left FW. Its mission was to root out terrorist and prevent attacks: it participated in live events, obtained intelligence to fool plans of different corporations (for example, Revan's) and so on. So, even without the FW side, it did plenty of things for the Empire.
What of corporations that free slaves for the Republic, like EM? Or maybe scholars and other venues that have existed in the Empire? Or the Scope for the Gallente? There are dozens of ways of supporting your empire beyond FW, and forgetting or ignoring those sides of the coin is limiting everything: you very well stop RPing and dedicating to FW killing alone if that's all that matters to be loyal to a faction.
And OOCly, what for those people that don't like the game mechanics involved in FW? Good examples for not liking it have already been suggested here. Do they have to forcefully do something they are bored with (which would, eventually, lead them to getting bored of the game and leaving) so they can RP to be loyal? I find that completely against the base of the game, which is to have fun.
So, to sum it all up, in my book that claim is clearly a "no". Of course, if you RP being loyal and do nothing for your faction, then I probably will see you ICly as the classical person that only pays lip service to his values. But, then again, Seph does consider most of the capsuleer community is composed of self-centered egotistic maniacs, so he wouldn't be surprised.