"Western-Backed"?

Maybe you've heard about the protest going on in Lebanon right now. So far I have heard the current government of Lebanon (the one being protested) referred to as "western-backed" about a half-dozen times. This is from the New York Times and NPR (my main news sources).

I wonder why they don't refer to the ruling coalition in Lebanon as the "democratically elected government". Yes, they're also backed by France and the USA, but that's not why they are currently in power.

Hezbollah is making a power-grab in Lebanon. They couldn't get power in the elections (possibly because the system is set up so that no one group will dominate; possibly because the majority of the electorate doesn't want them to...) so now they're trying to take power by mob rule. This isn't about the west. This is about Hezbollah vs. the rule of law in Lebanon.