I'm not completely following the ins and outs of the currency conversion arguments. However, the majority of my BRGs are for Australian hotels against websites that quote in non-AUD. Each and every time I change the currency display on Hyatt to whatever the competing site is displaying and compare that way. That is, rather than changing the competing website to AUD (to match the default rates (home currency) displayed on Hyatt), I change the display on Hyatt to whatever the competing site is displaying.
I've never been denied because of the reasons I think suite2suite is outlining. That said, it may well be because the competing rates I'm finding are in currencies that Hyatt displays. InIherebyresign's case, Hyatt doesn't display the rate in MXN by default but it seems it is possible to select rates in MXN if you wish.