Pretty much all Charity Navigator is good for is determining how much of a charity's funds get spend on fundraising. Everything that's not a fundraising expense is therefore a "program expense".
You don't really HAVE to go to 3rd parties for this. To their credit, the Wikimedia Foundation publishes their own financials, as audited by KPMG:
https://upload.wikimedia.org/wikipedia/foundation/1/1e/Wikim...
You can browse the breakdown of their expenses on page 5. It does seem like hosting their websites is only a tiny portion of their total expenditures. This is their own published financial statement, hosted on their own website.