First, respect for you as a former kettlebell-sport guy. I'm a kettlebell enthusiast.
Second, I agree with you...sort of. A brief aside: I was a football player and wrestler in high school who dabbled with powerlifting/O-lifting, a football player in college that achieved sorta-respectable numbers all around, and then...shifted to long distance running from age 22-27 before coming back around to a strength focus, and I am dallying with the idea of going into KB sport myself. I agree that doing a little top-end strength work on my deadlift and power clean because that 53-pound bell will feel a lot lighter to me once I've rebuilt my power clean to 225-plus and my deadlift to 405-plus than it does now (I just posted about this in my training log yesterday). So I can buy a little of the "anything physical got easier when I got stronger" statement, but...even that statement has limits. It's one of those things that sounds good on paper and is easy to agree with, but "anything physical" in that context really should be "anything where strength actually helps me."
A marathon is a physical activity; getting stronger will not help you run a marathon (really, try it, or ask some of the CrossFit goons that tried to claim you could run a marathon on CF and dropped out, or limped to the finish line in 4 hours behind 60-year-old graybeards). Swimming is a very physical activity; but somehow I doubt Jim Wendler would recommend 5/3/1 to a college swimmer.
Ergo, "getting stronger will make you better at anything physical" is really a saying that sounds good on a strength website, but we should realize that it has limits.
Flipping tires, pushing the Prowler...I mean, of course that has more carry-over to kettlebell sport than regular running would. But kettlebell sport and a Tough Mudder are not the same thing! In kettlebell sport, you have to give maximal effort for about 10 minutes, lifting a weight that is still a darned heavy object. It requires "endurance" of a kind but not the same kind of "endurance" that. I would argue that KB sport is still closer to the "strength" end of things than the endurance end of things.
In contrast, a Tough Mudder will take a good athlete at least 2.5 hours, possibly as long as 4 hours, and the only "strength" it requires is the ability to pull your body up, around, and over things; while it does require to keep running up and down hills, for stretches ranging from a quarter-mile up to three-quarters of a mile, 20-25 times depending on the specific course (every TM is different).
Those two activities require a very different type of endurance.
Some things fit neatly into a single definition: running a marathon is unquestionably an "endurance" activity. Powerlifting is unquestionably a "strength" activity. But things like KB sport, or a Tough Mudder, exist somewhere along a spectrum between those two things, and to lump them into simple bins with a statement like "Pushing the Prowler helped condition me for my endurance sport" without considering the type of "endurance" involved in KB sport vs. a Tough Mudder (KB sport is plenty hard - but in the balance of "strength" vs. "endurance" and, even moreso, the TYPE of endurance required) is just silly, and you're smarter than that.