Reading is the most important skill in the sense that if your reading is strong enough, you don't need other skills. (That's not my phrasing. It comes from Yuan Zhou, but I like it.) But no one's reading is perfect. Even computers can't exhaustively check all variations in anything but the very late endgame. That's why we have proverbs and joseki books and other lore. It's to help us make some kind of choices in situations where reading is not possible.
Most beginners can barely read at all. So for them, big benefits can be gained by using proverbs and understanding some rules of thumb. Direction of play is one of those things.
But as Bill pointed out, there aren't exactly a lot of 7-dans kicking around that struggle with 10-kyu tsumego. (But there are 10-kyus that can answer 7-dan opening problems.) Most of the gap between 10-kyu and pro is reading. But human reading is not like computer reading. We don't consider the following and then read out bazillions of variations to the end of the game:
$$W Read it out...?
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- Click Here To Show Diagram Code
[go]$$W Read it out...?
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You never know. This might be the best move.

So reading includes choosing better candidate moves, and so it assumes some knowledge of go theory. For that reason, it's possible to argue that reading is inseparable from knowledge, at least in humans. Studies in chess at least show that stronger players choose better candidate moves when reading. They prune the tree better, so much better that they often don't even have to go deeper and would rather spend time judging the end result of some options.
But they can go deeper if it's needed.
Brute-force reading is helpful or even necessary in some constrained situations. Ladders, enclosed life & death, some critical cuts and connections, for example. Because of the nature of go, it is often the case that mistakes in those situations are especially costly.
So when I say reading is more important, I can only say human reading, which is informed by good knowledge and infected by bad knowledge at the same time.