>If you concede that your computer has a chip with DMA access which can be used by the government, then you must concede that the same chip can monitor you for activity that triggers active surveillance.

Whats DMA access? Direct Memory Access access?

That aside, I'm not willing to concede that across every computer than has been/can be built and be exploited by a government out of the box remotely [because dragnet] (most of them, I will concede probably can though, and conversely anyone technical enough can probably exploit many systems in the same way for their own means[don't trust your spouse/freinds/employees?, bug them with remote backups of data to analyze in real-time, hell, companies do such things now as-a-Service]). But continuing on with your conclusion of a dragnet (which is more or less present today), access isn't really the problem, but you have a signal and a noise problem, wherein you will have false positives and false negatives. Text book example of the mal-possibilities is the NSA providing data which led to the targeting phones in the ME, which drone strikes we're initiated and hit innocent civilians[0]. Just wait when we're at the point when this is happening within a countries national borders by domestic agencies, one day, someone is going to be taken out that wasn't meant to be taken out. Can't ignore the false neg/positives forever, though governments seem to try very hard to do so. I think corporations are more forthright about the extent the data they collect is able to be used because if you knowingly contract/ utilize bogus data for certain applications, someone else will eat your lunch eventually.

>activity is fitting the pattern of some kind of criminal activity

From a predatory-prey/evolutionary standpoint, criminal activity is always evolving (typically every living being and the systems they rely on are).
Not to mention the time sensitive nature of these systems that do the analysis so if $criminal_activity is always changing and over a defined period of time, you risk that you will get no signal for those who conduct such $criminal_activity in less than the defined period of time or that by the time the analysis has been done, or any signals collected from such device will be moot (i.e. computer was destroyed, thrown away or even worse: passed along to/associated to someone else which also means any point there after associated with such systems is akin to going after a ghost within the machine).

>Is there really any technical knowledge that could protect you?

Well since the focus is on tails [but mostly on the dragnet], one can clone the sc[1] and go through it for what could possibly define one as a Tails user, replace that with something else, build their own image and voila, you just avoided being in the dragnet. The thing about dragnets is that they can only really capture the lowest common denominator, deviate only slightly from that, and the adversary will have to expand resources going for an targeted operation (any adversary, not just nation states is technically possible of doing these things and by definition not a dragnet). This is what happens today. Not in some far off distant dystopian future meant (intended or not) to invoke fear in the ignorant/lazy. Yes if one wants to avoid being in a dragnet with some of the tools they use, then one will take the steps necessary to keep such information obfuscated/opaque from the dragnet.

[0]: http://www.policymic.com/articles/16949/predator-drone-strik...

[1]: https://tails.boum.org/contribute/build/