Just as a recent example-- McVay gave a lot of details about the personal conversation he had with Puka about his off-field incidents. About how Puka was remorseful and apologetic, and how McVay was going to put his arm around him and help him make more mature decisions, etc . etc.
IMO McVay only says "I'll keep that private and between me and the player" when things do NOT go well. As I recall McVay used the "I'll keep that between us" line when he was having troubles with Akers, and also after the Ernest Jones trade.
But when a personal conversation with a player goes well, McVay is happy to share details. If Stafford was enthusiastic about the Simpson pick, there would be no reason for McVay to decline to comment about it.