I'm surprised that a 24 person study was considered large enough for the FDA. I've only worked with 'proper' medical devices with much greater potential for harm, but I'm used to trials involving 100s to 1000s of people.
This is a difficult trade off. If everything went through a PMA as currently defined, we would have a tiny fraction of the devices that we do today, and they would cost orders of magnitude more. The FDA is trying to balance access to beneficial technology with risk, and it isn't an easy line to draw.
Regarding safety: You absolutely have to show safety. Any new material, additive, or processing chemical used for an existing indication must be demonstrated to be safe. This also applies if a currently used material is used in larger quantity, or used in a more serious degree of contact (longer duration, more invasive). This is done through biocompatibility testing in accordance with ISO 10993.
510k isn't a loophole, shortcut or less safe in any way. Clinical trials are unbelievably expensive, hundreds of millions of dollars or more. Often so much so that they are prohibitively expensive for alternatives to therapies that already exist or for patient populations that aren't large enough to make back the initial investment. Without the 510k pathway much of our modern medical treatment portfolio wouldnt exist as drugs and devices for only the very most lucrative health problems would be cash positive to develop.
Thanks to 510k devices thousands of lives are saved every day, and therapies that were once too expensive for the masses can now be afforded.
We're finding the chance that the study will demonstrate brain eating. The hypothesis is that brain eating is rare: .01 chance of that. So any particular subject will probably not display brain eating: .99 chance of that. Assuming brain eating tests are independent, you can raise that quantity to the hundredth power to get the chance that all 100 subjects will not display brain eating. That would be a failure of the test, so subtract that chance from unity to get the test's chance of success.
My math: If there is a 1% chance of something happening in a given sample, there is a 99% chance of it not happening. So, for a set of N samples, you multiply 0.99 * 0.99 * 0.99... N times or 0.99^N to determine the chances of it not happening in any of the samples. 0.99^100 is about 0.37. 1- 0.37 = 0.63.