("No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.")
Not comedy. One reason for "quartering soldiers" was to obtain evidence and to intimidate within a private space. I've long held any form of broadly imposed in-privacy monitoring (including compulsory back door keys) is a 3rd Amendment violation, especially if the individual is practically paying for it.
Wikipedia and news articles should give you the details.
I'd say lack of access to law (as well as its unbearable complexity) is an issue of due process and the fundamental rule of law.
But you can't look to the Constitution to dictate everything - its drafters could not anticipate all future developments, and if the government is that citizen-hostile a piece of paper won't stop it. That which the Constitution does specify should be considered more as "behavioral tests", and currently the majority of our test report is failure.
The counter-point presumably being that law enforcement are not soldiers? Maybe the 3rd amendment has been interpreted as applicable to all government agents.