My speculation on why david spiked the drinks abridged version:
David: Sir, we have discovered some black goo that seems to have extreme mutagenic properties it seems to allow the creation of life out of no where. It is highly probable that it is what allowed the rise of humanity in the first place.
Weyland: can it save my life?
David: we are not sure, its properties and structure are so complex that i/we have no idea how it will effect a human. It can do anything from fixing you to dissolving to into your base genetic pieces. The technology is so beyond us that we can make no accurate predictions.
Weyland: Find out, if our machine can't give you an answer, try harder.
David: Yes sir, i will go find out what it does to humans.
David: Well shit, that didn't work...
David: Dr. Shaw, we are gonna have to freeze you in carbonite, i am sure whatever comes out of you will be interesting, but we have better stuff to do, so you just sit tight. Here's a tranq shot.
Weyland: Why Hello Dr. Shaw, we are just gonna go see my maker, wanna come along? why, egads, you are covered in blood! and your stomach is stapled together. Whatever, i have barely days to live so i am gonna go ahead, come along if you can.
Weyland: So what did you cut out anyway? Well whatever, just make sure you didn't throw it out, we will dissect it after i get my genes fixed by my creator.