Well I checked Haist and he says nothing about letting photographic solutions, including D-76, stand after mixing other than to allow them to cool to working temperatures. So that's Haist, Kodak and Ilford. I'm convinced.
Let's be clear on a few things here:
1. OP is mixing XTOL which does not contain HQ
2. We cannot compare the stability of mild-pH solvent developers such as XTOL and D-76 with that of low-sulfite staining formulas containing Pyro or Catechol.
3. Concerning developers containing HQ (D-76 etc):
a) Note PE says a tiny change due to the consumption of dissolved Oxygen and formation of HQMS in developers containing HQ. This is probably all within the margin of experimental error when developing film. Not sure what measurable effect if any this has at the working pH of fresh D-76.
b) PE points out this depends on the amount of dissolved Oxygen present in the first place. OP says he's using distilled water, which to me means he's pouring it relatively gently from some vessel, not spraying it from a fire hose and then violently mixing it.