Muay Thai fighters train Muay Thai. Baghdad versus Erosa is an example of why it's not always so simple, and why Muay Thai doesn't necessarily always translate to best stand up when the fighting isn't done under Muay Thai rules.
Baghdad is, at the very least, a competent MT fighter. The org he's champion under is obviously not the most reputable, but never the less he's fought and beaten Thais, and fighters who've beaten Thais. He's not world class, but he's not average either. Yet he got tooled in stand up by someone very unorthodox, even though that someone isn't exactly the shining beacon of striking ability. The only reason he lost was because it wasn't a Muay Thai fight, it was a MMA stand up fight. He would have knocked Erosa out in a Muay Thai fight in seconds. I'm not sure how much easier to understand I can make it.