Liz, as you wrote, I am almost certain that the U.S.A. does have in place regulations of the type suggested in this report for the U.K.

What do I think? I agree with the Companion Animal Welfare Councils summary:
..... the bigger centres, those run by charities, commercial organisations or public bodies, should be required to obtain a licence from their local authority, granted when certain conditions are met, including agreement to an annual inspection.
Smaller rescue centres and refuges, it says, should not need licensing, but ought to register with their local authority, which would be able to offer advice and send inspectors with the power of entry.
The balance seems about right to me, depending on what they mean by 'certain conditions', I am always wary of officialdom maybe becoming too officious!