No, more like when someone buys an FX35 it shoudl say 350Z on it as well. It's all the same platform.
Think of the 350Z and the G35 like the new Explorer with, and without, the 3rd row option. Other then having two extra seats in the rear, very little is different between the two. Both are sold in Japan under different names. It's all apart of Nissan's attempt to decrease the number of platforms they have, so with the introduction of the new V35, they introduced the Front-Midship platform, which was later used to build the Z33 and FX (whos chassis number I can't think of right now). Suspension and drivetrain are all the same, with minor tweaks to each to give a different feel. The bodies make them look different, but they aren't without the body.
Same deal with the ST, Ranger and Explorer. Take the body off and they are all basically the same, using the platform introduced in 1983 on the Ranger.