The "distant" sound, however, is probably caused by the lack of bass response in that mic. Bass dissipates more quickly than higher frequencies as distance increases. Thus, people often perceive a lack of bass frequencies as being indicative of distance.
Just to be clear, I was only pointing out that the second sentence about bass dissipating more quickly is incorrect. The opposite is true.
As you correctly note in the first sentence, there are issues relating to proximity effect and mike response that can come into play.
There are also issues of human auditory perception as you point out in the third sentence. The threshold of audibility is about 60 dB higher below 100 Hz when compared to 1 kHz! Basically, we can't hear bass until it gets medium loud. Since increasing source distance does reduce SPL, distant sources may seem to lack bass if the volume is much below 80 dB SPL.