Unrelated to the tea, but cold water is somewhat safer to drink than water coming from your boiler, that's why.
I think the theory is that "stale" water lacks sufficient oxygen for tea brewing to fully brew or something.
I'm not a big tea drinker, but I am definitely not a super fan of water that's been sitting out a day. There's not been time for stuff to grow in it yet, but it still tastes gross.