Here's my experience with mine. As the current owner of a 3800 with a tilt-bed on it, my best guess is that the hydraulics were added after the factory.
The best evidence I can find for that is that mine appears to be a dealer, after-market, or possibly an owner add-on based on the fact that the ends of the frame were cut off using a torch (pretty ragged cut at that). I would expect a "cleaner" frame end if it was a factory install. I've also not been able to find any factory documentation on hydraulics for 3800-series trucks but I've found a couple of after market references on tilt-beds. My experience on dump boxes for larger trucks (during the late 60s to mid-70s) was they were always added after the truck was delivered to the dealer (my Grandfather was a F*rd dealer) or that the hydraulic setup was added to the factory platform or stakebed.
On mine, the hydraulics were manufactured by "Harsh Hoist" not too far from the original owners farm, as I have recently found out. It's about 70 miles between Brush, CO where the truck lived most of its life, to Eaton, CO where Harsh is still headquartered. It's a double ram setup using the PTO from the transmission and other than the cuts on the frame ends, looks like a pretty professional installation. You can see one of the rams in the pictures that are in the Gallery. The best that I can figure, is that mine was an original platform or stake bed (haven't been able to determine which) and that the hydraulics were added later, possibly at the dealer before delivery, so that the wheat farmer didn't have to shovel the contents out of the bed.
Anyway, that's what I've found so far. If anyone knows different, please feel free to correct me and set me on the path to greater Stovebolt enlightenment.
Welcome to another 3800 owner!