The easiest way to understand this is in terms of mutual information.

If we both flip a coin independently of one another, then both coins have a 50%/50% chance of being heads/tails and the distributions are independent of one another and thus uncorrelated, but imagine the two coins are initially attached to one another, flipped, and then we separate them. Now they're both still 50%/50% for heads/tails but are perfectly correlated, so they are guaranteed to have the same value, and so if you know one, you know the other. In this case, the coins are said to have mutual information on one another.

It turns out in the physical world that mutual information, or more specifically quantum mutual information (QMI), plays a very important role. The marginal statistics on the behavior of a system can depend upon whether or not it shares mutual information with something else. You see this in the double-slit experiment because if you record the which-way information of a particle, then necessarily it must have interacted with something to record its state, and thus whatever measured it must possess QMI between itself and the particle, and thus the particle's marginal statistical behavior will change.

This is in no way unique to human observers or human measurement devices. You can introduce just a single other particle into the experiment that interacts with the particle such that they become statistically correlated and it will have the same effect.

QMI is rather counterintuitive because you can establish QMI in ways that you would intuitively think would not impact the system being measured. For example, you can have an entirely passive interaction whereby only the measuring device's state is altered and not the particle in order to establish QMI between them.

You can also establish QMI without an interaction at all, such as, imagine that the measuring device is only placed on 1 of the 2 slits and you only fire a single photon and that photon is not detected. If it's not detected, you still know where it is, because it must have traversed the slit the measuring device was not on. Hence, the non-detection of something can still be a detection and thus can still establish QMI.

Intuitively, you would think a passive measurement, or a measurement that does not even involve an interaction at all, should not alter the system's behavior. But the mathematical structure of quantum mechanics is such that the system's marginal stochastic behavior is genuinely statistically dependent upon the quantity of QMI, and so things you would intuitively believe should not affect the system do, in fact, affect the system.

You can even use this effect to detect the presence or absence of something without ever (locally) interacting with it.

In the Mach-Zehnder interferometer, the photon can take two possible intermediate paths, we'll call them A1 and A2, but both end up at the same place. Then, at the end of the experiment, it can take two possible paths again, B1 and B2, with a detector placed on both paths. You find, in practice, that there is a 100% chance the photon will show up on B1 and 0% on B2, unless you block either A1 or A2 with your hand, then it will have a 25% chance of showing up on B1, 25% chance of showing up on B2, and 50% chance of not showing up at all (because it was blocked by your hand).

The reason this is interesting is because, without your hand blocking an intermediate path, there is a 0% chance it will show up on B2, but with your hand blocking one, it changes to 25%. Thus, if you measure a photon on path B2, you know with certainty that someone's hand must be blocking A1 or A2, yet, clearly the photon did not traverse the path of the hand or else it would have been absorbed by the hand and you would have detected nothing. You thus can deduce the presence/absence of the hand from a particle's behavior that never (locally) interacted with it, and so logically speaking, the hand must be having a non-local influence on the statistical behavior of the particle.

This influence is due to the fact that if the particle interacts with the hand, it will be absorbed into it and slightly will alter the states of the particles in the hand, and if it does not interact with the hand, it will not do this. Thus, you could in principle look very closely at the particles that make up the hand and deduce whether or not the particle took the path the hand is on based on whether or not this alteration occurs, and thus there is QMI between the hand and the particle's path, regardless of whether or not the particle actually interacts with the hand. The mere presence or absence of this QMI changes the particle's behavior.

My understanding is. Every method of measurement influences the results.

I'm in cognitive sciences not physics. But it applies there as well.

The measurement method always interferes in some way with the result.

I have used this example with helping students understand research methods.

Doesn't matter how "non-interfering" you think your method is.

In some way or another, the act of measuring or the device used to measure (or both) changes the thing being measured.

shy proton theory

My understanding is that the tools that are used to observe it cause the wave function to collapse. Like how putting a thermometer into meat to check the temp makes a little hole.