Unless it was possibly a proof-like business strike with frosted devices like this one. I'm not 100% sure, but I think these may be rarer than proof CAMs and DCAMs.
The 1956 Type 1 is one of the most difficult coins in cameo/dcam (partly based on the scarcity of the type 1 itself) and it commands a strong premium. The 1956 type 2 however is affordable (this one is more common with cameo as this was near the peak of the Mint's prowess in cameo coinage until the 1960s*). *See here for more: https://coinweek.com/modern-coins/why-did-the-number-of-cameo-proofs-increase-1950-1964/
From my experiences with NGC, the grades of coins I submit always get graded lower than what I think. I guess that's owners wishful thinking. I've got several ICG graded coins and when compared to comparable NGC and PCGS coins the grades are higher; not to say that they aren't nice looking coins.