I’ve tried booking through hotels directly and it’s never been cheaper. It is so weird. I usually end up using hotels.com which is just one of many booking services owned by Expedia.
Have to call them -- they often have contracts that mean they can't offer cheaper rates online, but are happy to over the phone. Though it's possibly down to where you're staying I guess, but I've had good luck doing that in Australia, the UK and a couple places around Europe!
And worst-case, they'll match it usually, and I'd rather be booked directly to avoid the crap that the article is discussing