Even though I know that this thread is going nowhere fast and will spend eternity bogged down in trolling and people arguing about the concept of probability instead of actually adding their data to the pool, I shall on a whim throw my hat into the ring.
1) Discussing the concept of "impossible" is irrelevant to this discussion. There is a non-zero probability that your arm will spontaneously drop off due to random subatomic particle movement, however this probability is absurdly low. This is what we call, for convenience, "impossible"
2) Discussing the concept of "random" is also irrelevant to this discussion. Computer programs do not generate random numbers, they generate an arbitrary number based on a seed input, in this case, unknown. It was once thought that bacteria were a spontaneous and randomly occurring phenomenon. Once more data were available, it became clear that they were not.
3) Due to there being a relatively large number of viable group compositions, if in fact loot distribution is skewed based on group composition, across a large number of groups of varying compositions, the skew will be obscured, moreso if the bias is generated by a transient influence (e.g. last two numerals of the server clock are even means there is bias, just as an arbitrary example). This means if Bioware were to look at loot drop metrics overall, it would appear to be pretty much pure RNG.
Anyways, with that blathering out of the way, here are my records to the extent that I recall them.
I have done a large number of solo runs through Normal flashpoints on each of my three characters. Across every single run, 3 in 4 loot drops were appropriate for my character's primary stat.
As for hard modes, my usual group is Juggernaut, Marauder, Powertech, Operative.
In ONE run, only Powertech gear dropped.
In TWO runs, only a single piece of Willpower gear dropped.
In every other run (I've lost count, quite a few), TWO OR MORE pieces of Willpower gear have dropped.