Since I've never experienced your "too revealing" problem and have had a ton of CD/SACD players -- from $60 Toshibas to my current $3600 Oppo/Modwright -- I have to believe the problem lies elsewhere in your system. Without knowing the components of your system, though, it's impossible even to generalize.
One thing sure, IMO: It is NOT "just the nature of the recordings."
One thing sure, IMO: It is NOT "just the nature of the recordings."