Oooh ... that's a bit confusing, I find. The microphone's directional behavior doesn't change based on how far it is from the sound sources, but the makeup of the sound field at the microphone surely does.
I would emphasize that a microphone can only pick up the sound field that's present at its location--or some selected portion of that sound field, based on the microphone's pickup pattern. The farther a microphone is from the sound sources in a reverberant environment, the more the sound field at the microphone will consist of diffuse, reflected sound rather than direct sound. "Diffuse" characterizes both the arrival times and the angles of arrival. It's those sound arrivals that become increasingly "omnidirectional" with greater miking distances, in that their angles of incidence become more and more nearly random; the microphone doesn't become any more "omnidirectional" itself.
At the same time, at greater distances the microphone's diffuse-field response (i.e. all angles integrated, and taking its directional pattern into account), rather than its on-axis response, increasingly characterizes the sound that you'll get with it. This is precisely the situation in which a small, high-quality single-diaphragm supercardioid microphone excels over larger microphones of all kinds, dual-diaphragm microphones of all kinds, and/or other directional patterns. (Actually a pure figure-8 has the best match between on-axis response and diffuse-field response "all other things being equal", but surely you don't want rear lobes that are as sensitive as the 0-degree pickup when you're far away from the sound source.)
I know that I say this often, but I still feel as if there are people who aren't paying attention: This is why shotgun microphones are such a poor choice for indoor miking at substantial distances--their diffuse-field response at high and upper-midrange frequencies SUCKS. At such distances the angles of sound arrival are mostly random, and the interference tube simply adds coloration rather than filtering out reflections. The tiny residue of direct sound at the front of the microphone is buried within all the other front-arriving sound, and the interference tube can't tell them apart.
By contrast, a good supercardioid (I'm very fond of the Schoeps MK 41 V in this respect) has a diffuse-field response that isn't very much different from its on-axis response. The MK 41 is a little brighter in its diffuse-field response than the 41 V is, if you want the kind of "distance compensation" that EmRR is talking about, and its response is flatter up to frequencies which I no longer hear, but that some people still do.
--best regards