The question is can they do it to everyone frequently, including the handful of super-nerds out there who love tracing every operation their devices do and can be certain they don't have some sort of malware? While I don't see the capability as technologically infeasible, I do think it would be noticed sooner or later if it was always-on.
If such a feature does exist, then it would have to be used sparingly on targeted individuals, and even then if it was used to incriminate them such evidence would have to come up in court (unless they all get the s/Gitmo/secret prison/ treatment, a big assumption!) and then the world would know such features exist. Presently I think traditional manners of evidence-gathering are probably sufficient and people publicly leak all sorts of data (or have a lot of data logged that can be subpena'd) -- plus every now and again we hear about some nerd (https://news.ycombinator.com/item?id=5194489) reporting they have been bugged. Some people think the CPUs of Intel et al. have backdoors in them, but if so, there'd be no need to bug computers.
Absence of evidence is evidence of absence... so I don't really take the government backdoors in everything by default too seriously. I'd need some sort of evidence showing their existence to change my mind.