SPOILER :
I think Voldemort did in a way. When Severus first goes to Dumbledore he's in tears and begging that Lily's life be saved (pg.543-544) and old Dumbles uses Snapes love of Lily to get Severus on his side after Lily and James die: "If you loved Lily Evans, Truly loved her, then your way forward is clear".IMO, I think Ol'Voldie could trust Severus because they both had rather disturbing childhoods (I'm sure at one point or another Voldie must've searched Severus's mind about, well, everything), along with they're equal hatred of muggles/mudbloods (except for Lily).
Ahh! But if Snape had killed off Dumbledore, then without doubt the DeathEaters would have known that Severus had done it then poor Snape probably would have died anyway.
I wouldn't at all be surprised if there's a sudden increase in "Snape is the true father of Harry Potter!" fics on the inter-web.