Yeah, I don't think Anakin's conversion was ever doubtful. Problem is the execution. Just going by what you see on screen, it doesn't really make sense. It's not hard to give it some perspective.
Part of the problem is, Lucas doesn't know how to make us feel about Anakin. In Ep. 1, Lucas fixates way too much on how cute and special Anakin is, and never sets up any indiciation that Anakin's too special and self centered. Having him win the podrace in an underhanded way and then allowed to slide by the Jedi would have helped.
In Ep. II, we do finally see some real raised questions about Anakin's maturity, but Lucas handles it all tactlessly. When Anakin's showing his "dark side" tendencies, it's obvious to the viewers, because he's acting like a spoiled brat and we instantly side with Kenobi. What would have been better is for Lucas to have found a way to show us how ridiculous and unfair the rules of Kenobi and the Jedi seemed to Anakin, before zooming out to show us how Anakin's choices were leading him a certain way. At that juncture, self-righteous mini-rebellions of the Jedi and Kenobi would have sufficed, and been much more effective than the spur of the moment sandpeople rampage.
For episode III, Lucas could have delved way more deeply into how Palpatine leads Anakin to the darkside by appealing to his frustrations with the Jedi and leading him to abandon the Jedi religion. There was AMPLE opportunity for Lucas to raise the alternative "Sith" perspective, but he just never does. After watching Ep. III, the whole Sith religion and it's philosophical reasons for violently rejecting Jedi are still vague, at best. The only clear reason for why Anakin rebels is wanting to save Portman. Anakin going dark isn't really made obvious to us by an outward rejection of the Jedi religion, but just through a series of heinous and overly violent acts he commits because he wants to do whatever the Emperor says.
So while I agree with the writer, I don't agree that Lucas does a good job of making the conversion make sense.