A definite no. I would never trust important information with small companies, they have a much smaller threshold to abuse it or forgo proper security since they have much less to lose.
But you'd trust important information with companies like AT&T? I mean, I don't know, maybe you don't. It just seems to me that a smaller company can instantly lose if a security breach is exploited, but larger companies with gigantic market share can/will continue to operate after such an event due to massive PR machines and consumer inertia.
