Google™ fights to avoid genericide.
“Genericide” is when your trademark becomes a synonym for a thing or activity. Asprin was a trademark once. Xerox™ and Kleenex™ live on the edge of genericide and spend big bucks to prevent it.
If “to Google” something were to come to mean to search for it online regardless of which search engine one used, google or “googling” would have become generic, destroying the trademark — and meaning that competitors could use it too. At present it still clangs a little to say “I googled him on Yahoo” so I think the brand is not yet generic.
But they sure are right to be worried.