Excellent posts. I suppose the only thing left to mention is that knights are armored and ready to fight. Pages are menials and lackeys who have to be respectful and aren't going to be trusted with super-important messages (maybe a few "meet me at the north tower!" or flirtatious flowers, but nothing like "the enemy is invading!").
So, if a page has a message, he'll run up to you, kneel and say, "Message sir/madam...." and eagerly tender it to you. Anyone at court, after all, can shout, "Page! Take this message!" So, very much, a letter, email, phone call just telling you some quickie information or something fun/flirtatious. Nothing someone would be afraid to have read or intercepted. And pages are ready to take back a response as well.
But a knight arrives there on horseback (speed across a great distance) and in armor. This is a commanding message or an urgent message--like the enemy is attacking from the north!--and you'd better respond nicely/quickly, because the knight means business. You offer an insult and the knight, the king's own messenger, might run you through. You refuse and there might be mortal combat or disaster. This message is important, and the knight makes sure that no one intercepts it, because if it is intercepted, if the knight dies and the message is read by someone else...that's the end. He'll also take back a message to his master, but it better be equally important. He hasn't time for anything frivolous.