The correct call is No Call. The BR ran exactly how the Safety Base Rules-makers envisioned. The F2 and F3 both went "outside" and used the orange (safety) base; as a consequence / allowance, the BR must use the opposite, in this case, the white base. Furthermore, the BR was within or on the chalk of the baseline all the way until the last stride, which takes him(?) to the white base... which he has to touch by rule, since F3 is squarely on the orange base. And he didn't even interfere with the (poor) throw from F2, either.
Granted, NFHS wrote into the(ir) rules that F2 doesn't have to throw to 1B to enact RLI being called on the BR, because TPTB don't want to have throws deliberately aimed at the BR's body, but even if NFHS is applicable here, on this play/game, it's not warranted on this play, since the BR, again, is not outside the lane until the last stride.
The PU shouldn't call RLI in the first place. That "fixes" it right there. Otherwise, I don't see any other umpires on that field that could refute the call. Either this PU is working solo, or the BU is at C; in either case, the BU is in no position to contribute any information on this, other than perhaps a cursory consultation of rules knowledge. Furthermore, I can tell from body language and conduction alone – this PU was dead-set-convinced on calling RLI. Consulting other umpires on the crew (when they're present) ain't gonna change much, if at all. What's needed is a PU who knows these applicable rules better / more effectively, and can interpret them properly.
To run exactly how this BR ran. This particular PU booted it.
If you're going to explain anything to kids, it's "don't swing at a pitch that's in the other batter's box".
He shouldn't have been called Out. Simple. Do nothing different – other than the aforementioned "don't swing at pitches that grossly outside". Carry on.