This is very frequently repeated, but I have never encountered any reason to believe it is true. Certainly, better science has been seen to win, in cases, but the amount of shit hurled first has always been enough to drive any sensible person to do something else less likely to attract hurled shit.

We can get a sense of how often correct theories are suppressed by looking at cases where a now-accepted theory was anticipated decades or even centuries earlier, but failed to gain traction at the time, not for lack of evidence, but simply because the evidence was unwelcome.

Theory of causation was understood a full century ago, but suppressed by the statistics mandarinate, and is only in the past 20 years starting to resurface. Evidence conclusively demonstrating human presence in the Americas before 15kya is still routinely dismissed. Requirement for surgeons to wash their hands took decades to catch on; to this day, more hospital ICUs have the traditional 4% incidence of fatal infection than the very gradually spreading 0%. The entire lack of any negative health impact from eating saturated fat was well demonstrated decades ago, but has only been accepted in this decade. These are just cases I know about; most have been better interred.

I am forced to conclude that there remain many more successfully-suppressed correct theories than accepted correct theories, and that things are getting worse, not better. I.e., correct theories still win sometimes, but the fraction of correct theories that win is decreasing in the face of tenured grant committees.