Sean, I agree - given one source (O'Sensei), we have seen a plethora of aikido offshoots. Why? My belief is that all of them...and all of us...do the right thing by passing on what they (or we) know of Aikido, after long, personal and arduous study. And this will necessarily result in many flavors; and I don't equate this with dilution, in the way I think Eugene is speaking of, and I think Eugene would agree.
My only beef is that I think it impossible to really know one's Aikido until one has removed the impediments to what Toyoda Sensei used to call the discovery of "your true self." He also used to say, with proper training, it did not matter what one did - everything became an expression of one's own art. And he was adamant about owing one's own Aikido, not forever aping him in empty replication.
But along with urging his students to "make our own Aikido" was our absolute commitment to him and to constantly work the forge, constantly seek to return to the moment - in other words, constantly let go of one's facile notions or surface understanding while pursuing the budo he offered. In other words, paradoxically, in order to eventually own an expression of the art, one first had to commit to ridding oneself of attachment to one's own idea of it; this is the subject of many other threads and literature on the relationship of zen to budo. And, I think he was right...I see it when I see people of budo, such as Chiba Sensei...nothing mystic or veil-glazed eyes, but I see a deeply truthful power and kiai in stillness from these Shihan that cannot come, I truly believe, but by the path they followed.
These Shihan did not talk their way through to an understanding of O'Sensei's Aikido - apparently, this was an impossible feat because, as you say, O'Sensei often lost his students in his religious and philosophical discourses - they simply worked their asses off and eventually their body owned it, their "deep self" owned it, and they created their Aikido.
So, that's my quick (and I hope not flippant) answer as to "one source, many versions." All true, but all began first with direct transmission and absolute commitment to a master.