Well....a good shot is a good shot regardless, still takes skill to make it.
Often these places will have a mix of birds, captive bred and trained birds that are for falconry and display, but also support re-introductions, treatment for injured wild birds that will be kept wild and set free again once they've healed, some feeding of wild birds. They can keep rare or endangered species going through breeding programmes etc. Some birds require a lot of care and because of that become domesticated and therefore can't be released so it's not a straightforward issue.
I think the line is if it's portrayed as a shot of a wild bird, but in this case it's clear it was taken in a centre so perfecctly fine IMO