I think Feynman was maybe a bit too harsh, possibly because he was so used to the relatively pristine world that physicists get to live in that he outright balked at the noise psychologists and social scientists have to live with.
You do get noisy measurements. That's why you need to pay a lot of attention to your confidence intervals and standard errors - they give you a sense of your signal to noise ratio. Not all psychologists and social scientists are good at that, and that's a problem, but IMO it's really not _that_ difficult to distinguish babies and bathwater here.
And I think Feynman's comment about between-subject designs is outright dangerous. You do not necessarily reduce your noise by switching to within-subject designs. You just move your noise to a place where it's much more difficult to measure, and possibly create a lot of endogeneity that you can't deal with except by throwing out a bunch of assumptions and hoping you're right. Sure the numbers that spit out of your equations start looking more tidy, but that doesn't mean your results are more trustworthy.