Well, I assume the leaked-thoughts-pensieve-memories were a part of it, but, I don't know. I always assumed Harry would keep Snape's secrets in death as I think he did in life, even if it was only to protect his parents' (and his; explaining how he found out would be tricky) reputations.

(As for being secretive, he was mentored by Albus Dumbledore! Need more be said?)