"But in such models we are usually confronted with the problem of multiplicity of equilibria"

Even with perfect competition you run into the problem of multiciplicity of equilibria due to wealth effects. So it's feasible that there may be numerous 'natural rates' (where peopple choose different levels of labor/leisure at various real wage rates). I think that's why it's better, for the purpose of macroeconomic policy, to focus rather on the NAIRU then the 'natural rate'.
On the other hand if you interpret Friedman's remark to mean simply that cyclical unemployment must be due to disequilibrium in the labor market then you're fine.