They certainly don't have the kind of relationship that could justify the GNOME Foundation running their women's outreach programs for them. GNOME's absolutely miniscule compared to both of them, in terms of money, developers, staff, users, everything. To put this in some perspective, the Mozilla Foundation alone has approximately 3 orders of magnitude more income than the GNOME Foundation, so it's no surprise the majority of GNOME foundation cash flow was for the Outreach Program for Women rather than for GNOME.

I could understand if, say, Mozilla decided they wanted to help other open source organisations that were only tenuously related to them in this way because they can afford to, but the GNOME Foundation is simply too small to take on this kind of big project.