I still don’t get why Linux Foundation helped Google out of that.

I could be wrong, but I think that (at least to some extent) the Linux Foundation exists to be the more corporate-friendly face of Free Software Open Source, as a reaction against/in opposition to the hard-line "end-user freedom" stance taken by GNU/the FSF. If that's accurate, it doesn't surprise me that it would take a soft position regarding Google's monopolistic practices. Especially since Google is a gold member of it.