No, surveillance and ads aren't "threats" in and of themselves. Being surveilled or shown ads doesn't itself harm you (modulo wasting your time/brainpower, but by that logic getting an email or a phone call is also a threat). What would be a "threat" is potential harm occurring as their consequence. In the case of NSA surveillance, for example, people are worried about innocent people getting caught for the wrong reasons and due process not being followed, resulting in wrongful legal/physical/etc. harm to the wrong person. Or in the case of Equifax, one possible harm is your SSN leaking and being used for ID theft (financial harm, until if/when you prove your innocent).

Now what I'm not seeing is exactly which company's DNS is avoiding what credible harm that people here believe is potentially likely to result from using Google DNS.

As far as Google (or any company, really) internally is concerned, the fact that they are merely "using" the data for themselves (to show you ads, or whatever) is not itself a harm to you. (And maybe worth mentioning, they have used a lot of information to make life a lot better for everyone, like location for traffic data.) The harm would be if they used it to (say) discriminate against you in advertising goods/services, or to harass you, or if they did not secure it properly and your data leaked, etc. None of these are things I'm aware of happening inside Google, but if you know of evidence of this happening, I would love to know.

As far as Google is concerned externally, the only threat you seem to have hinted at here is that you believe they are likely to sell your data to other parties who are then likely to abuse them (such as by harassing you directly, or sharing/exposing your data online to others who might harm you). I have seen no evidence that this has been the case with Google (or Facebook) either -- which should make sense given that you believe user data is their most important asset -- but again, if you have any, by all means do share.

Given the above, combined with the facts that (a) so many people here seem to be disregarding the actual privacy policy, and (b) for most people Google probably already has more information to screw you with than your third-party DNS provider ever will, I'm led to believe there isn't really anything to be gained by avoiding Google DNS. But to each their own...