I don't think the OP got a fair hearing. Pinch is maybe a bit too loose in terminology. Let's try to read his mind.
If I might speak for his notion, GR says that a stress-energy tensor is the source of gravity. Traditionally you'd lump in there all forms of energy including rest masses of particles, electric field stresses, etc. Yes, even the electron is a source of gravity in GR, with m0c^2 in the T00 term and it's electric field in the EM tensor, nonzero at least along the diagonal in a rest frame I think.
Now *if* you postulated that space-time had a certain energy density and *if* you assumed that the particle masses and EM energy densities had their origin in this same energy density (Higgs?) and *if* space-time were an elastic medium such that concentrating some of it ("pinching") meant straining it near the pinch in accord with the Einstein equation, *then* maybe the pinch model might be onto something. I think maybe one of these assumption has a case. Most are not going to hold any water.
At best it's a nice mental extension of the overused rubber sheet analogy. I like it but I don't think it works.