Even worse, both of these ideas, while obvious "crackpot" territory, are much more believable and less fantastical than the claims of most of our current religions, which most people in the world still believe. So as long as we continue to respect peoples' religious beliefs, I have a hard time with dismissing these ancient aliens/advanced civilizations claims out-of-hand.
First, if you have the ability to engineer a bioweapon like this and spread it around to eliminate cancer in humans, why wouldn't you just genetically engineer the humans to not have cancer (i.e., just bake the ability into people, instead of having an airborne agent which will have much less efficacy since not everyone will catch it)? And secondly, why would you want to give people the suffering that comes with colds?
So, that leaves 2 possibilities: 1) Cold viruses were engineered, but they evolved to their present state where they're actually a big nuisance rather than a big help, or
2) Cold viruses were just a natural evolutionary outcome.
Either way involves cold viruses getting to their present state through evolution (both ways being undesirable to humans), not engineering, and #2 satisfies Occam's Razor better because of what I wrote at the top (i.e., engineering contagious viruses to fix a problem in human biology is a Rube Goldberg-esque solution).
I guess if you really want to get wacky, you could postulate that in this ancient society, they had some sort of religion or philosophy that humans shouldn't be biologically "tampered with", so either most people or at least the authorities would have rejected a straightforward medical solution, so some rogue person or group came up with the virus scheme (somewhat similar to how we can't get everyone to actually update their software to fix security vulnerabilities).
(Perhaps all their recorded history was digital or otherwise ephemeral so we cant find it, assuming history repeats itself)