The cortisol and sex hormone receptors, the nuclear receptors, are all related and all diversified (almost like species of animals) from the same gene that got duplicated by accident in some individual animal's genome. That happened dozens of millions of years ago, before there were humans, or even monkies. And accordingly, all the hormones that bind those receptors are variations on the cholesterol molecule, with a similar overall structure.
GH is a totally different bird, a giant hormone 20 or 30x the size of testosterone or cortisol. So it cant directly activate the cis-acting glucocorticoid response element in XMRV's genome. The thing to wonder about is whether GH could alter XMRV's behavior indirectly, by increasing the production of things like cortisol, or cortisol receptor, progesterone, progesterone receptor -- whatever.