Apologies if I offered approximately this entry a year or two ago - I had the same experience and it struck me the same way, and I don't recall if I posted about it. But anyway.
Last night I had to take the F train all the way out to Coney Island for a Brooklyn Cyclones minor league baseball game. Today I had to take the F in the other direction, to Roosevelt Island for some early morning tennis.
Each time, a train that was NOT labeled an F train approached on the F track - a D train yesterday, and an E train today.
Each time the garbled PA system said something like the following: "This is a [D/E] train traveling on the F track." I had to make a snap decision: do I take the train or not? The trains that they were labeled as would potentially take me to the wrong place (actually, the D might have worked yesterday, but definitely not the E today). In each case time was of the essence. So should I board the train or not?
Each time I did and it worked out for me. But my view was that, if these trains were traveling on the F track and making F stops, then they were F trains. They were not, at least for the duration of the journey, D or E trains traveling on the F track. A train is defined by the stops it makes.
The MTA, by contrast, appears to be essentialist (is that the right word here?) about train definitions. It thinks of a train as a D train or an E train, if that is its nature or how it is labeled, even while it is traveling on the F track and making only F stops.
Perhaps they could have clarified things a bit, without necessitating the metaphysical dispute, had they said that the trains were "traveling on the F track and making all F stops." Then I would still disagree with them about what the trains really were, but it would have been immaterial instead of causing initial anxiety.
Then again, perhaps I am over-thinking the whole situation a bit.