... But, at a philosophical level, they are not measuring acceleration. They are measuring the charge in a crystal - or, more specifically, the voltage. As with most scientific measurements, when you drill all the way down, you are usually measuring only a few very basic quantities. In most cases, all you're really measuring is a displacement.
From there, you assume a model of some kind to equate that displacement to whatever you claim to be measuring. In the case of an accelerometer, a small mass of known value is assumed to accelerate and apply a force to a crystal, thereby causing a deflection of the crystal, which is known to produce a voltage proportional to the deflection. The deflection of the crystal can be related to a force, and the force can be related to an acceleration.
You're assuming F = ma is true. While no one is going to challenge that, the point is, if some mad scientist were going to do an experiment of some new hypothesis that claims something other than F = ma, you certainly shouldn't use accelerometers to make measurements for that experiment. When you're on the bleeding edge of science, you need to be very, very careful about those kinds of things.
Part of my career was spent working on machine control, and what I saw really bothered me. Controls engineer Carl designs a control system. Programmer Paul then turns it into code that only vaguely resembles what Carl designed. Test engineer Tim then goes into the lab and changes numbers until it appears to him the machine is stable. But what Tim does is just guessing and/or experience regarding which numbers to change. There is ... no guiding principle. And in the mind of an extreme empiricist (as I would label them) that's OK. In his mind he followed a scientific method. He has a hypothesis that changing a number from 7.3 to 9.1 will make the machine stable. He tests it. The machine tests stable. ...