I don't think anyone would disagree with you but that does not disprove a random walk. A random walk means that today your best guess for tomorrow is:
tomorrow's price = today's price + unknowable surprise
The fact that surprise for stock A is related to surprise for stock B does not disprove a random walk.
Sorry for the geek outburst. I do think lots of other things disprove it, at least for some stocks and indexes some of the time, but that doesn't.