Alfred Pennyworth is Agent A.
GIW uses letter aliases.
Imagine the absolute and total misunderstanding of Danny just beginning to trust the bats only for one of them to let that codename slip. Imagine they offered for Agent A to patch him up. Or mentioned him over comms.
Either way Danny isn’t trusting that for a second.
Alfred managed to get Danny into medical care anyway through sheer force of will and the Disappointed Grandpa Look (tm)
"I was in her majesty's secret services."
It took Danny a second to process that through the panic and looklooklook for an exit thrumming in his veins. "..what?"
"Essentially I was a spy, for England during the wars, back long before I met the Master and Mistress Wayne, my code name is simply a retaking of that mantle for security purposes. It has nothing to do with anything to do with the government here." Alfred kept his voice low and calm, explaining and it was slowly soothing the panic Danny was feeling. At the same time, he was keeping Dick and Jason back, Tim seemed to have been delving into research, likely from something Danny had muttered without realising in his panic.
"Why the fuck did we not know about these? These violate so many fucking federal and international laws, what the fuck!" Jason's reaction soothed the final panic.
"You didn't know? With all the calls to the league, how did you not know?"
"Danny, what calls?"
Bruce and the kids getting so much Grandpa Lore dropped on them today!
It took them years to learn so much. Danny gets this information straight from the source in his first month here!
This is favoritism!