Evidence? In what way is Google trying to be like Apple? They don't even sell hardware! They're entirely different companies going after (for the most part) completely different markets.
Not "entirely", but close enough. ...and yes, unless you live under a rock, Google does sell hardware. They don't make it, like Apple does, but they do try and hawk a handset now and then.
The point isn't even worth arguing given it makes so little sense, but.. Apple shouldn't buy Google because it is not close enough to their core business. The two companies compete in a few select markets, but Google is a predominantly a search company and Apple is a software company. They compete for browsers (not a money market) they compete for desktop OS, they compete for mobile software and now they're competing with handsets. They do not compete in each other's core market.
Apple has multiple revenue streams (hardware, software, mobile), Google for the most part has only one (search). With ad revenue not booming like it was, Google's growth will (already is) slow; Apple's is still accelerating.