The fact that Ubuntu is open source wouldn't change anything if those things were true. Just because you can look at the source does not mean you're looking at the source of the code you're running, because you almost certainly did not compile the whole Ubuntu distribution from the source, rather than that, 99+% users just downloaded the precompiled iso and installed from the official binaries, where a backdoor could slip by and you'd be none the wiser even if you did the insane task of reading all of the code you're running (which is not possible for a single human being) and then there's also the fact that you can slip a backdoor that even a great programmer wouldn't necessarily notice at a glance while looking at the sources, so there is that.
The crux of the matter is, you can't trust your computer.
Even if you did trust nearly every single human being involved in the process, it just takes a compiler writer to break the chain of trust.
http://cm.bell-labs.com/who/ken/trust.html
Open source means you can have a look at what it actually does. So yes, after all it means that it will most probably do what it claims to do, because everyone (at least people who can code) could check and it takes just one person to have a look at it.
The crux of the matter is, you can't trust your computer. Even if you did trust nearly every single human being involved in the process, it just takes a compiler writer to break the chain of trust. http://cm.bell-labs.com/who/ken/trust.html
http://c2.com/cgi/wiki?TheKenThompsonHack