That's a bit of a stretch. The core OS as delivered from the distribution, sure, of course excluding services not on your system given by the distro, just a bit of tinfoil but who's to say Canonical isn't handing over your search terms and other user data from Unity for example? It's already going to Amazon, why not the NSA too? And no, I'm just pulling that out of thin air as a hypothetical example.. if it were true you wouldn't know. But after the fact? No. Any OS can be compromised regardless of who made it, especially since you would theoretically run software outside of what was given to you out of the box to begin with, even on Linux not all of some very common software is open source, and that's completely ignoring the obvious issues that can be done as malware. That's discounting any unproven tin-foil conspiracy theories of course.
The point was using OSS in such a case provide assurances that your system cannot be compromised by a unknown backdoor installed by a 3rd-party vendor.