Sorry, logic is faulty - in that scenario the head end of the spur cable would be subject to the sum of maximum loads downstream,
So: 3 13A sockets on a spur could justifiably result in 39A total load.
This is not what we are talking about - we are talking about a single socket ona single spur which leads to a design current for the spur of no more than 13A.
A fault that does not trip the circuit protective device - a fault that happens to cause L-N currents to flow that are greater than 20A but insufficient to trip the 32A breaker?
That would be a very specific and unlikely fault. It also invalidates the whole possibility of using 2.5mm for spur wiring or even rings themselves as the design criteria for any part of the ring is that the cable shall be rated for 20A or greater (for the purposes of conductor sizing, derating and grouping).
Given the IET have decided rings and spurs in 2.5mm2 are OK based on 20A components being protected by a 32A protective device, I am more than happy to use a parallel argument for justifying my assertion.