Be sure to distinguish between the current return cable from the welder (typically clamped to the workpiece) and the electrical ground (usually made through the EGC to the welder chassis and possibly NOT connected to the workpiece in any way).
The welders must not connect their "ground" (actually return) clamp to a local ground reference (building steel or whatever is handy) and assume that current can flow at a low voltage drop through whatever (if anything) is grounding the workpiece.
Tell us more about how the welders are connected and what the "whatever the machines are grounded to" is. If the workpiece is in fact solidly grounded and the current return clamp is connected to the workpiece, what you describe should not be happening.
If for some reason the welding current is flowing through the welder EGC or through a casual metal to metal connection, what you are seeing is likely to happen, and that is why that configuration is not allowed.