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).