I worked for several SRV manufacturers for well over 20 years and I would certainly advise you to take the manufacturers claim of "full open at set pressure" with a grain of salt. Direct Spring SRV manufacturers have spent hundreds of thousdands of research dollars throughout the ages to try to get valves to open faster (or rather open with less overpressure). It is precisely because the valves do not open fully at set pressure, that the overpressure rules were written into the codes (this applies to gas applications as well!). The AGCO Series 80 and the equivalent model from Flow Safe Series have gas valves that open fully at set pressure, but no such animal exists for liquids. Special liquid trims and valve configurations have been introduced in the last 20 years to get better performance in valve opening vs set pressure. The Crosby JLT trim is such an example. But what it comes down to is this: It really doesn't matter what the SRV manufacturers' claim. Sizing of the relief valve is based on an allowable overpressure - 10% for most codes such as ASME VIII, API 520 etc. Even if the valve were to open at less overpressure or even at set point, you can NOT take credit for it in the sizing, so you get no advantage of any such claim. What the SRV manufacturers have found out, is that the liquid trims do improve or shorten the blowndown (difference between opening and closing pressures). The only way to get a liquid pressure relief valve full open at set point is to use a modulating pilot valve. The valve will throttle open with the pressure remaining constant until full lift is reached.
One other idea to pass along. The definition of set point on liquid service varies from manufacturer to manufacturer. It is generally not defined as the first onset of liquid flow but at some sustained flow. For example, AGCO-Crosby define liquid set point as an uninterupted flow stream the diameter of a pencil. Why do they all do this? - there is a simple explanation. Because the ASME code criteria for valve capacity certification is based on 10% overpressure (single valve, no fire), or 16% overpressure (multiple valves, no fire), or 21% (fire case). Since thwe valves have to be full open at the 10% overpressure to acheive consistent, guaranteed flow rates, delaying the "liquid set point" definition makes it easier to acheive.
