Aren't we oversimplifying here? There is more than one scenario to reivew.
Consider that the relief on the oil pump is set to an specified pressure (not "absolute" in deffinition of pressures in engineering speak, but more like "fixed" in terms of gearhead talk). In other words, the pump relief may be set to say 150 psi. Unless the backpressue gets to 150 psi, the relief will never open.
The oil filter may or may not have a bypass valve in it. The bypass valve works on the concept of pressure differential, and not an absolute "fixed" concept.
If there is no bypass valve in the filter, the only relief available in the system is the pump relief (or some component failure in the system like a burst filter housing or a blown seal). In this case, the relief will only open if the total system backpressure is, in this example, 120 psi. As long as the backpressue is not exceeded, the filter will flow as much or as little as the pump provides, assuming the filter's total flow design is greater than the engines flow design. In a very wide assumption for my example, it's typical for a filter to be rated around 7-9 gpm, but the pump may only be putting out 3-4 gpm, so the flow of the filter is not an issue.
If the filter does have a bypass valve, then you must consider the differential pressue and total system pressue seperately. If the filter has a bypass setting of 15 psid, then as long as it doesn't see greater than 15 psid, the bypass won't open.
Two examples to consider.
Ex 1) the engine pump relief is set at 120 psi, and the usual pressure in the system is 50 psi at steady cruise. The pump relief won't open. But now think of the filter bypass. If that 50 psi reading is taken upstream of the filter, and the media is blinded off to a point where more than 15 psi exists across the media, then the BYPASS valve will open on the filter, even though the relief valve in the pump didn't open. It would take a LOT of stuff to plug the filter media like this, but that's why it exists. It keeps the oil flowing to the bearings, although unfiltered. If the filter had no bypass valve, and it plugged off to the point where there was a greater and greater pressue, it would eventually build up to the 120 psi and the pump relief would open. The problem with this is that oil which is bled off at the pump relief never gets to the bearings; it's dumped right back to the sump (pan). If the filter has a bypass valve, it would open on a 15 psid, and the bearings will be getting "dirty" oil, but that's a heck of a lot better than little to no oil at all.
Also, in this scenario, consider if you have an actual gage on your dash or just a little red light. A gage can show you a low or high pressure, but a light only typically comes on when low pressue is sensed. If you have just a light, and you have an overly high pressure, you'll not know it. Even with a gage, you would likely see a high pressue reading on your dash gage, and you might assume that the engine is getting a lot of oil, but in actuality, the engine bearings are getting little to no oil at all because the pump is dumping right back to the sump; NOT GOOD! That's why a gage is better than a light, and why gages are marked with both an upper and lower acceptable range.
Ex 2) on the other hand, consider the system at start up and/or during the first few minutes of operation. The oil is very thick. The pump is trying like heck to push the oil. The oil is not only thick on the upstream side of the filter media, but on the downstream side as well. So even though you might see 90 psi at the "gage" where the pressue sending unit is, you're also experiencing a very high pressue all through the system. So the filter bypass valve is NOT open because (for the sake of example here) the gage might be showing 90 psi on the upstream side, and the downstream side might be at 85 psi. Because there is not a 15 psi differential, the bypass valve will not open. Now if for some reason the pressue were to spike (say you revved up the engine to 6k rpm by accident) the pressue might spike at the pump relief (and open), even though the bypass valve in the filter didn't see a 15 psi DIFFERENTIAL, and therefore didn't open.
The pump relief and oil filter bypass valves operate in concert with each other, but they each are there to protect your engine from two different scenarios. The pump relief is just that; it protects the pump from damage due to an overpressure condition. The filter bypass is there to protect the filter itself, and also the engine, by allowing dirty oil to flow, because dirty oil flow is better than no oil flow.
Flow is flow; pressure is pressue. They are linked by several physical properties. They have direct interaction, but they also have independent characteristics which cannot be ignored. You must be careful to consider the whole system and it's design, looking at individual components as well as features interdependent.
