The sample sizes are plenty large enough to infer statistical significance, there are numerous studies, and the odds of getting a yard on 4th and short are basically the same as the odds of getting a yard on third and short, which is quite common and is obviously game planned against. There is no real controversy here among people who have studied this. I know of no credible study that has come to the conclusion that's it's a good idea to punt on 4th and short on the opponents side of the field regardless of the score and time. There are dozens of good studies that show why coaches should go for it.
By numerous, you mean one modern NFL-specific one (Brian Burke's EPA study), and by odds, you mean none, as 3rd and one is simply not the same as 4th and one. Look at the defensive coverages used by NFL teams on a 3rd and one vs. a 4th and one: on third down they're just as likely to play 2 deep safeties as to bring one in the box, while on 4th downs they'll often utilize goal-line style packages with a single high safety. The Vikings put nine in the box on our first 4th down attempt.
Again, I'm not saying that the right idea isn't to go for it on 4th down, but the implication of Burke's study had more to do with the expectation of points scored vs. actual points scored, and required him to attempt to normalize that estimate across multiple eras of football, and with zero insight related to the quality of the teams or schemes involved. Let's say you're a team wanting to run for it on 4th and one vs. the '85 Chicago Bears or the 2012 New Orleans Saints. Are the probabilities of success the same against both teams? Hell no. Do the probabilities tell you otherwise? Nope. These theories that dictate that going for it on 4th down is the only right choice are based in a fantasy world where NFL teams don't dedicate hundreds of manhours each week trying to negate as many advantages for the other team as possible.
So, while I like that Rivera is willing to be more intutive in his 4th down decision-making, I'm not going to act like that is something we should be doing every single time the opportunity presents itself, as it will negate one of the advantages of the 4th down call in the first place: the element of surprise (which is again not accounted for in any way by those studies, which is a massive blind spot in their conclusions.)