The most common cause of a crash on opening a new tab is that Google Desktop is installed. Google Desktop has a setting to index the browser's history files. There is a bug in GD that when it does this with the IE7 version of these files, it causes a crash. Telling GD to not index these files (or uninstalling GD) should cause the crash on new tab to go away.
Firefox may not officially be Google's product but it is for all intents and purposes. Google has made Firefox developers fulltime Google employees who only work on Firefox. Hmm... Google also pays Firefox roughly $30,000,000 a year for making Google the default browser in Firefox.
I guess it depends on how you want to define the ownership of an open source project but Google is as close to an owner (and sugar daddy) as Firefox has... Do you think that the Firefox guys would go work on something that would make Google unhappy and jeapordize 30 million dollars or the paychecks of their key developers? Really.