May be how your's is strung. If you look at the saddle where the string comes up out of the block , you'll see that the hole in the saddle where the string comes up over, and the hole at the bottom of the bridge plate dont match up perfect on some of them, mostly on the high E and B. Mine has some play side to side on the high E. Ive done setups on 3 other reissues for friends over the last couple months, 2 Mexicans and 1 American reissue. Both the Mexican's had that issue, but the american didnt.

mines a 2001 classic 60's, the only thing that i can find wrong is that the holes in the back cavity cover don't line up with the bridge, the bridge is too far back. i have to dip the trem to get strings out.

No you shouldnt, you're right. BUt Im not convinced there's any problem with the neck, its just the way the bridge is. WHich is a problem in of itself