BA has chosen to permit ESA's on flights to/from the USA under policies much more "liberal" than those required by the US DOT and implemented by other carriers such as AA. DOT has proposed new rules which would vastly curtail ESA accommodations and require that they meet the strict requirements of a service animal. But, those rules, if issued, are likely at least a year away.
One can't criticize -- or ought not to criticize -- OP for taking advantage of the particularly generous conditions offered by BA.