This is somewhat ahistorical. The concern was patent licensing fees and it impacted way more than just Google.
H.264 is (and pretty much all MPEG standards are) a patent-encumbered format. Anyone who encodes, decodes, or otherwise uses the format needs to pay licensing fees to a confusingly-named patent pool called MPEG-LA. Google is entirely capable of paying those fees; random webmasters and Free Software hackers are not.
The only reason why this didn't become as much of a problem as I'm making it out to be is because the H.264 pool had a very affordable or zero-royalty tier (can't remember which) for free Internet video distribution. At one point it looked like MPEG-LA was going to shitcan this tier, which would have basically killed every video site at the time except for YouTube. This wasn't an empty threat: previous ISO-standard formats like MPEG-4 Part 2 didn't come to an agreement on web video, so it was never used on the web. Macromedia wound up licensing On2 VP6 (WebM's predecessor) in Flash specifically because it had no known patent encumbrance.
Today, we have H.265, which is a licensing nightmare even for premium video providers and hardware manufacturers that are ordinarily used to paying licensing fees. AFAIK it's something like 3 patent pools and a bunch of other companies now?