As Bill said a few posts earlier, "pressure is pressure". It doesn't matter if the fluid is steam, water, Bud Light, or some combination thereof.
The key mistake in your analysis is that you confused pressure with force when you said:
That should be, "The force is .0274 x 125 = 3.425 lbs."So the pressure on that is .0274 x 125 = 3.425 lbs.
But since that 3.425 pounds of force is acting on an area of only .0274 square inches, it still results in a pressure of 125 PSI in the water, which then results in a force on the 1-square-inch piston of 125 pounds.
-- Russell Mac (not a physicist, but I'm pretty sure I've got this straight)
Note: This ignores the fact that the pressure within a body of fluid increases with depth due to gravity.