The dealer may be BS'ing you.
If the car was advertised as a Z51 but does not have the option, you've been "had". Make sure you have a copy of the advertising which said that.
If the car was equipped as such, "Z51" would appear on that label.
It's possible the previous owner put drilled rotors on the car, and this dealer either out of ignorance or out of malice, told you had Z51 because they saw the drilled rotors and with the presence of the drilled rotors, figured you wouldn't confirm the car truly had the option
Here is a list of equipment which should be on the car along with the cross-drilled rotors
Higher rate springs
Larger diameter front and rear stabilizers
Specific shock absorbers
Engine oil and power steering coolers
Special transmission ratios if it's a manual
Performance axle ratio if it's an automatic
Goodyear F1 Supercar EMT tires...although it's possible an '06 would not have it's original tires.
With the exception of the tires, if any of that stuff is missing, the car is not a Z51.