It's all part of the Lattice of Coincidence...

Here's what I just learned:

"The name 'U-Bet' dates from the late-'20s, when Fox's grandfather got wildcatting fever and headed to Texas to drill for oil. 'You bet' was a friendly term the oilmen used. His oil venture a failure, he returned to the old firm, changing Fox's Chocolate Syrup to Fox's U-Bet. He said, 'I came back broke but with a good name for the syrup,' his grandson relates."

The source cited is a conversation between David Fox and the authors of "The Brooklyn Cookbook", if anyone cares enough to check it. Frankly, I'm perfectly content to believe this without more rigorous proof.