> This is confusing whether it can be blocked and whether it would be effective.
It shouldn't be confusing because its really fairly simple.
The gist is this... so long as determinism as a systems property holds true in a system, you can leak information by the absence of something when compared to another expected thing. This is how inference works in many respects, you have properties and you can deduce or infer from whether those are present additional information that is not necessarily given.
Most gifted problem solvers probably couldn't tell you that is what they are doing because its unconscious often a result of years of observation.
Computers fundamentally require certain system properties such as determinism to do work in the first place, and you can inject non-determinism into those processes in ways that won't break underlying subsystems as long as its within an expected range and that can make it indeterminate. An indeterminate fingerprint is useless.
In the case of outright blocking the code from running, you leak information that you are blocking it by preventing it from running since they expect a range of values back and a null (the response when nothing gets sent back) is itself a value (or state if you want to be technical).
The site then only has to test for this semi-unique case (i.e a null represents a single group of people who are blocking it) and then prevent the site from responding to you. They are the gatekeepers because they control their infrastructure.
Incidentally this is how almost all the Are you human tests work. It collects an intrusive fingerprint, and if its within a range that corresponds to a known user spectrum of values then it allows you to continue to the site.
This is a rough boiled down explanation, it can get quite a bit more abstract and technical when talking about whether determinism is present (i.e. how do you test for it).
Ultimately, if you can understand determinism, you fundamentally understand the limits of computation and how computers work at a barebones level. It also gives you the ability to find whether certain types of problems are impossible (and thus you don't waste your time on them, or unproductive avenues).