I have two "Sweet 16's" and neither have it carved into the wood stocks. It is however engraved into the side of the receiver. It sounds like someone had some time on their hands to carve this into the wood.
These are GREAT shotguns. My father, brother and I all have a kind of a love affair with the Browning A5/Remington Model 11/ Savage 720. The Sweet 16 versions are a lightened down verson of the A5 16 gage and in my opinion, the best of all the Browning A5 designs.
I can honestly say out of all the shotguns I own, the Browning Sweet 16 is honestly my favorite for hunting, skeet/trap and sporting clays.
One note of caution: All parts except the Butt Stock, Forearm, friction rings, Bolt and Barrel will interchange between the Browning A5 16 Ga and the Sweet 16. The Bolt and barrel were both lightened up from the standard A5 16. The stocks were made of a less dense wood as well as dimensioned just a tad thinner and smaller. The friction rings and fricting ring spring also have a different temper to them to adjust for the lighter gun weight. The receiver was lightened up via metallurgy and not via dimensions from the standard A5 16.
Even if you can find a beater Sweet 16, they are worth getting and restoring to what ever degree you wish.
The one thing you will usually find broken is the forearm near the receiver side. Past owners fail to seat the barrel well enough when placing mag tub nut back on. This allows a little bit of slop for the forearm to be slapped against the receiver. The cracks are usually this and travel about 1/2 way up the rear of the forearm and can be fixed really well with bedding compound.
All in all, if you can find a shootable Sweet 16, get it, even if the exterior is FUBAR.
Good Luck
PS- There is nothing like going for morning grouse or dove than with a nice Sweet 16 in your hands.