They do, however, have a lubrication engineering department complete with their own lubrication engineers. They are responsible for designing the John Deere oils, greases, hydraulic fluid, etc. The lubrication performance is designed for John Deere equipment. Both Hy-Gard fluids are multi-viscosity fluids with high-viscosity index, and both contain about 3% zinc as an anti-wear additive. The hydraulic fluid also has friction modifiers for correct clutch engagement. Do other hydraulic fluids meet the requirements? I don't think anyone knows as has been previously pointed out - there is no independent agency that certifies compliance with a specific standard for hydraulic oil.
Here's my question. How much does your piece of equipment cost? Are you willing to pay the repair price if you use a non OEM fluid - and that fluid causes wear and/or a malfunction? Personally, I think it's foolish to attempt to save money on the single fluid in a tractor that runs all of the hydraulics and transmission.