Mounted units have fewer people to do the on-foot work which COIN requires, period. The Math applies so there's some validity due to that factor in the historical precedent...

Still, Steve and Cav Guy have it right IMO -- the good Commander (branch immaterial) will do good stuff, a less competent one will fail with the right kind of unit. Like MattC's tag line says:

" 'Give a good leader very little and he will succeed. Give a mediocrity a great deal and he will fail.' - General George C. Marshall."