I don't care what the FM2n manual states about this; I've done my own very careful testing with my own specific filters and predominant film choices. Nikon did offer its own version of a red filter (the R60), a little on the weak side compared to most 25's; and the reading with this particular filter in place would probably be at least half a stop off; and the recommended 3 stop filter factor is basically correct based my own experience.
But what happens when you have a red-orange 23 filter in place, like I sometimes use on my Nikon? It's brighter to view and focus through than a 25, but distinctly stronger than a deep orange 22. Then there are stronger red filters like a 29, really nice for cutting through haze with TMX, but which might require a 4X filter factor depending. This is why personal testing is important.
So what Nikon states is correct in terms of THEIR OWN limited filter selection, at least in relation to most black and white films, but certainly not all, since metering with contrast filters in place fails to take into account differences in spectral response between various black and white films. In other words, their advice is valid as a generalization; but there are numerous exceptions to generalizations.
For example, the real world filter factor difference between TMax 100 and Delta 100 with a medium green filter in place is half a stop, even though the meter reading itself would make no such distinction. Throw in Acros 100, which is orthopanchromatic, and you're a full stop off. This isn't the fault of the Nikon meter, which uses a silicon cell quite similar to that in Pentax and Minolta spotmeters, but demonstrates how films themselves differ in filter factors. And even the same filter number might differ somewhat between different manufacturers, or lot to lot within the same manufacturer.
And what one can get away with in a moderate contrast scene might turn out quite disappointing in a high contrast scene, where there is less latitude for exposure error.