It's because the opening and closing of the main valve is completely controlled by the pilot, and the pilot only sees the upstream pressure. Thus, backpressure has no affect on the pilot's action to open or close the valve. When the system pressure exceeds the set pressure, the pilot is commanding the valve to open, regardless of the amount of backpressure present.
Non-pilot conventional valves are completely different. These valves operate based on differential pressure, thus they are affected by upstream pressure and downstream pressure.
In a balanced PSV, there's a mechanical element (either a bellows or a balanced piston) which blocks off a portion of the top side of the disk (shielding it from being exposed to the backpressure force), leaving an equal amount of surface area on the bottom and top sides of the disk. The backpressure is therfore acting on this equal amount of surface area (top and bottom of disk), results in the net effect being zero. The backpressure force is balanced, acting equally to open and to close the valve. But a balanced valve can only tolerate a finite amount of force (backpressure) without experiencing mechanical damage. If the backpressure is higher than that limit, then a pilot valve is needed.
At some point you're limited by differential pressure between the PSV inlet and backpressure. The valve may open 100% and stay due to the pilot, but if backpressure = inlet pressure, no flow will occur.
I expect you'll relief calculations will show a much larger main valve will be required if you have significant backpressure so you can achieve the desired relief capacity.
Backpressure is two components, the superimposed backpressure (if you have a relief tank at x pressure, or whatever the case may be) and built-up backpressure that occurs when your PSV opens and flow is occurring. Your relief calculations should be calculating the total backpressure (these two items added together).
A large total backpressure means your valve has to physically get larger to flow the same capacity due to the smaller differential pressure across the valve.
You mentioned "70% backpressure", I was just reminding you regardless of PSV type you need differential pressure across the PSV to achieve flow.
The relieving capacity of all types of PSVs (including pilot PSVs) becomes affected at the point where the relief stream is no longer choked at the PSV orifice. In almost all vapor/gas installations, aside from those in which the PSV is set at very low pressure, the stream is in fact choked at the PSV orifice. The rule-of-thumb is that choking occurs when the pressure is being reduced by ~50%, but the actual value will vary depending on the composition and conditions of the stream. It varies depending on the fluid's Cp/Cv, MW, and temperature. The key point is this: As long as the stream is choked across the PSV, backpressure has no affect on the flowrate through the PSV. Choked flow means the fluid velocity has reached its maximum limit (it's sonic velocity). The intuitive notion that increased backpressure reduces the flow across the orifice only applies for streams that are not choked.
So, for all types of PSV's, one needs to know whether the backpressure is so high, or the set pressure is so low, that the stream is no longer choked. And BTW, if the dP across the orifice is so low that the stream isn't choked, then you have to use a different equation for calculating the PSV capacity (ref: API 520 Pt I). The standard equation is based on the assumption that the stream is choked at the orifice - and again, that's typically true.
The unique thing about a pilot operated PSV is that the valve remains fully open as long as the upstream pressure is > set pressure, regardless of the backpressure (actually, vendors will cite a max backpressure limit of ~90 to 95% due to internal friction between the main valve piston and the guide).
