The idea that you get a lot of just marginal significant results due to "P hacking" , i.e. minor fiddling with excluding outliers or picking a certain hypothesis test over another is probably true. Then there is positive publication bias i.e. only publishing positive findings.

However looking in the abstract doesn't really address either of these .. as even absent either P hacking or positive bias you would still expect the abstract to contain the selected highlights (i.e. positive findings) from the paper. It is the bit of the paper where you really should have positive selection bias!

If the paper has lots of negative tests (and most biological papers will report lots of negative control p values) these aren't picked up. A better way to see this problem (and I believe it is a problem) is to look at the whole paper and view the peak of margin results) compared to the whole set of p values.