I kind of thought that too. It seems to me that when you have the front wheel pushed against something, then you've got the front wheel itself pushing rearward on the bike (like when you pull the front brake.) Because the forks are angled, this is going to cause the bike to push down in the front (and thus want to raise in the rear) because of component vectors and shit. During the Neolithic Era (eg, when On Any Sunday was made) they had front suspensions that would actually raise up when you pulled the front brake, but these went out of fashion very early. My suspicion is that they caused the front wheel to have less grip when braking, but I've never ridden a bike with that setup so I'm not sure on that.
All that aside, if the engineers say chain tension puts downward force on the rear wheel I guess I have to believe it, but I'm not going to accept the "put the front wheel against a tree" thought experiment as evidence, because of the other factors at work.