I have been unable to find any authoritative (i.e. Blizzard) resources that describe how loot drop works. Where are people getting their information?
No, all information is based on Diablo 2 knowledge(where we had access to game files) and quotes here and there from Blizzard employees(blue posts, Interviews, tweets etc.) confirming it works the same way in Diablo 3.
An example of this is when Jay Wilson was asked about Tresure Classes and diminishing return on Magic find:
Jay Wilson: I don’t really know how to answer the treasure class one, lots of areas have different treasure classes but we try to make areas relatively equal depending on challenge and monster level. MF is not capped, though. Source
Because of this answer we know that Diablo 3 still uses the Tresure Class system that was used in Diablo 2.
I don't think you will ever find an authoritative source from Blizzard who actually gives a detailed description of how their loot formula works. That sort of information is too sensitive, and if they were to give out the formula, players would find a way to exploit it to their advantage. Not to mention, there are clearly tweaks to it that depend on several scenarios (monster type, first boss kill, etc.)
So what you are seeing on this site, forums, etc. are just general observations. Random loot is random, that is the nature of this game and many like it. So take what is said with a grain of salt.
In one word : random. As a lot of people said on the Blizzard forum "this is why Auction house (AH) will be a huge part of the game."
I can't tell you the base chances of dropping blue/rare/legendary items but as you may already know you can use gems and/or items to give you extra percentage of chances to find blue/rare items.