Calling PBS and AP - two of the most highly regarded news sources - “blatent propaganda” says more about this comment than the article.
You linked the Wikipedia article:
The Houthi movement is a Shia Islamist political and military organization that emerged from Yemen in the 1990s.
In 2003, influenced by the Lebanese Shia political and military organization Hezbollah, the Houthis adopted their official slogan against the United States, Israel, and the Jews.
In late 2014, the Houthis repaired their relationship with [former president Ali Abdullah] Saleh, and with his help they took control of the capital city. The takeover prompted a Saudi-led military intervention to restore the internationally recognized government, leading to an ongoing civil war
As far as I know, even their allies Iran and North Korea don’t recognize them as the legitimate government of Yemen. I’m not sure where you got your information, but I believe perhaps you misread or misunderstood something that you read.