It was St Georges Windsor, so I think the chances of demonstrators getting anywhere near is remote.
And it was safe enough for the Queen and many other adult members of the British royal family, European royals, aristocrats and other VIPs.
Plus the Waleses live in the grounds, so he didn't have to go into public to get there.
(I agree that saying "minor seasonal illness" might have been better wording if illness is the cause).