At one point while I was at my dad's for Christmas, I made the mistake of trying to get an intelligent response out of my sister before she'd had tea in the morning. She refused to reply to my question until she got her tea –
I giggled gently at this at the time, but the same thing just happened to me: faced with a strange problem to investigate at work, I decided I couldn't face doing it without a cup of coffee to hand –
Another explanation is that it's like reserves. If her plane is gliding just above the treetops, and you say "can you do a barrel roll", she'll just not, but if you fill her tank up first, she can safely, even if it doesn't actually use any more fuel than she had before. That is, you don't want to get embroiled, but once you *have* tea, then you're safe, so you can start to wake up without fear of having to think without caffeine :)