I mean, if there is nothing to be suspicious of (i.e., nothing is out of norm) even then would they prefer to be pro-active and keep looking for something which *might **come up **someday *. Wouldn't this create a feeling of being interfered/monitored all the time?
I am not saying that Parents are perfect. They are humans too and can and do make mistakes. If they are acting the way you just mentioned (being suspicious all the times) then yes they are over doing it and hurting their relationship with their kids.
I think as a kid, we should go and talk to them about this. Open communication resolves lots of issues and if parents cant initiate the communication then kids should.