Dave just did a "Murphy's Law" on this op amp. He shipped a bunch of units using a 'slightly' different part number and the gadget went into oscillation. Best to order EXACTLY what is on the BOM. Down to the last letter...
The circuit oscillated because the design was flawed, choosing a part from a different manufacturer just exposed the problem.
I also agree on a general level, and the design would certainly not be right for a full-fledged, high-production volume lab instrument, but I would still cut Dave some slack on this.
When designing a decent precision device with such a low-cost, low-count part, low-power design, you have to make some compromises, which he did. Relying on very specific parts in that case may make sense, even though that can backfire at some point, and that is exactly what happened.
That said, the fact his testing never showed the problem (until he specifically worked on it) while testing the final units that he was shipping (I think he does 100% testing before shipping), obviously shows that the test setups were lacking in representativeness.
That warrants a suggestion for future video topics for Dave: one about the specific topic of power rail split circuits (and their potential pitfalls), and one about testing in general and designing test rigs that take reasonable end-user scenarios into account.