Yes, I think most statistical testing in science is flawed.
But, to be clear, the reason it could ever work at all has nothing to do with the methods or the data itself, it has to do with the properties of the data generating process (ie., reality, ie., what's being measured).
You can never build representations from measurement data, this is called inductivism and it's pretty clearly false: no representation is obtained from just characterising measurement data. Theres no cases where I can think of that this would work -- temperature isnt patterns in thermometers; gravity isnt patterns in the positions of stars; and so on.
Rather you can decide between competing representations using stats in a few special cases. Stats never uncovers hidden representations, it can decide between different formal models which include such representations.
eg., if you characterise some system as having a power-law data generating process (eg., social network friendships), then you can measure some parameters of that process
or, eg., if you arrange all the data to already follow a law you know (eg., F=Gmm/r^2) then you can find G, 'statistically'.
This has caused a lot of confusion histroically: it seems G is 'induced over cases', but all the representaiton work has alerady been done. Stats/induction just plays the role of fine-tuning known representatios. it never builds any