The opposite was the case. Mozilla was ditched by Google. It is logically that they say it the other way around, as it does sound much better, and gives the illusion that Mozilla is in control about their fate.
They got ditched after Google enforced minimalism (Australis) on Firefox with giving Mozilla "good design advice's" that of course backfired. And as soon as Mozilla's share dropped enough, Google gave them the boot.
Open Source is just an excuse to be able to fork others work and damage the source project with this.