No, Google asked the NSA to better secure Gmail because Chinese hackers compromised Gmail. They didn't hand over email to anyone.
Compare that to Microsoft and Yahoo just handing data over.
You're paranoid that Google could hand over data, and you miss the fact that every other competitor already has handed data over.
Did Google tell George W. Bush to screw himself when he asked for search data? Oh, yeah, they did. They are required to abide by laws (like the Patriot Act) but when they had multiple court orders from Brazil, they fought as long as they could so they wouldn't have to hand over information. Just like they fought against China to protect their users.
Microsoft, AOL and Yahoo just handed over your data.
Which company should you trust to do searches on?
Go ahead and trust the others. It demonstrates an amazing command of logic on your part.