You can’t just open a single faucet and be done. You need to open up at least 2, and preferably at different elevations with one being lower than most of your water pipes.

What this commenter is saying (I assume) is that shutting off the supply, and then opening just one faucet, you potentially trap whatever water is “below” that open faucet. Without moving water, those pipes can more easily burst when frozen. It won’t flood while you’re gone, but it can still freeze and then flood when you turn it back on.

What OP is trying to quickly describe is to empty your houses water lines completely before leaving. Then, with empty pipes there’s nothing to freeze. But not every house is the same, and in a somewhat typical 2 story house with a basement, shutting off the supply and then opening a faucet in the 1st or 2nd floor will leave the pipes in the basement (where it is coldest) full of water. It’s possible that the water freezing will expand up the empty pipe, and not “out” to burst them, but that’s not a guarantee.

Also, if you have water lines that feed a garden hose, which are not frost proof, those could very easily freeze and are almost certainly below a first floor faucet.

This is somewhat reckless advice as it’s incomplete.