It was my undestanding that they where law enforcement authorities equipped with wands of detecting illegal aliens and they don't know he happens to be a prince since the OP said that they visited the country "unofficially and his disguise with a small number of very powerful guards", so it was granting that they didn't know beforehand he was the crown prince (and might even not know later unless they happen to see the birthmark and to be knowledgeable of the birthmark thingie -- they might not know until they get a "sorry, we've misplaced our crown prince, and I think the person under a false identity you arrested might be him" letter).
The status with regard to the S-word is pretty irrelevant. I am pretty sure if Prince Harry tried to cross the US border from Mexico with a passport saying he's Joaquin Guzman, surrounded by heavily, militarily armed bodyguards, he'd be arrested and the UK wouldn't nuke Washington as a first response. Especially if the bodyguards violently resisted arrest.