Is Iran helping the Houthis to fight the Saudis?

All the western media propaganda channels claim that Iran is helping the Houthis to fight against the Saudi kingdom.

Likewise the government and media/TV of Iran also claim that they are helping the Houthis and the Saudi government who fight the Houthis likewise say the same thing.

However the Houthis themselves deny being supported by Iran, so why do Iran, Saudi, Israel and the USA all tell us the same lies and same fake historical narrative if they are independent of each other?

And why is Iran always portrayed as the opposition against the west+Saudi+Israel?

They want us to think that anyone who fights against America is doing so on behalf of Iran even while Iran is directly helping the American and Saudi military in every single conflict, as well as Zionist Russia and other enemies of Islam.

Iran is portrayed as the ultimate opposition when in reality they are the ultimate fake.

Is the Dajjaal worshiping government of Iran helping the Zaydi Mojahideen in Yemen? If so why does Iran itself have economic relations with the Saudi Kingdom? Why doesn't the Saudi Kingdom retaliate against Iran? Why have Iran and Saudi never had a war against each other? Use some common sense to see through their propaganda.