Ah, I think I found it. I took V to have a codomain in utilons in your example (that was my interpretation of "V is a random variable that depends only on u").

Reinterpreting the subsequent comments in that context, I can see that I was responding to "formally equivalent" in the original comment as if it meant "expected utility maximization of the traditional sort, where each outcome x is itself assigned a value by a function on x that does not involve V, will produce the same decisions as satisficing of the type described under these conditions."

Interestingly, the latter may be true if V did have a codomain in utilons (or at least, I was unable to come up with a consistent counterexample).