I would say the simple answer regarding Nimble Diagnostics is "no".
They seem to be mainly focussed on paternity testing and give very little detail about how their "ancestry" testing is carried out. It is very expensive and I cannot see any details on their web pages that indicate how the results would be much use to you. They only seem to talk about the nearly useless "ethnicity" type answers.
There is nothing (apart from ethics and maybe the occasional law) stopping law enforcement officers submitting samples to any of the testing companies under fake identities. If you don't want want to be compared then do not take any tests. If you make your test results private then you also cannot compare with others and so they become largely useless for your own purposes.
And, as far as I know, none of them "share" dna results with law enforcement; law enforcement run the same tests as other testers - as you noted in your original question.
Where they might share your actual dna with 3rd parties would be more likely with medical companies, but you have not mentioned that as a concern.