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I've read the little I can find online about Omaha High, and I saw the advice that I should always bet the pot if I bet at all.

Is this correct?

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This is a common expert opinion, but it's not universal. Furthermore, it only strictly applies to post-flop and turn bets. In Omaha, it's almost always possible (quite likely in fact) that one of (or a combination of) your opponents has pot odds to call any pot sized bet. The only way to minimize their pot odds is to bet the max (i.e. the pot). Of course this doesn't apply if you have a straight flush, quads, or the overboat (i.e. a QQxx hand and a Q55 board).

This never applies on the river because drawing out is no longer an issue. Feel free to make 1/3 or 1/2 pot value bets on the river.