Yup, will link to the podcast when it is published.
It is randomization and not only random sampling that was a key component of traditional frequentist inferences in the 20th century. Randomization may be random sampling or random allocation. The latter can be either natural (as in Mendelian randomization) or experimental as in RCTs. There is a very nice recent overview of the frequentist, Bayesian and fiducial paradigms here. Also, controversies regarding how much we can rely solely on the randomization procedure to license statistical inferences existed from the very beginning between Fisher and Neyman as nicely recounted here.