So I didn't want to answer this question because I wasn't 100% on it, but since its gone this long without getting an answer I figured I'd take a swing. Traditionally, the Mixtecs defined royal authority by appealing to one of several oracles who lived in temples/caves throughout the Mixtec region. They settled disputes between lords by performing divination and consulting the genealogical codices. In the late 11th century AD, the Mixtec lord Nacuaa found the oracles unwilling to support his wars of conquest. So he instead appealed to an outside authority - the Toltecs. He was granted a noble title by the Toltecs, which he used to assume supremacy over the Mixtec region. Other Mixtec lords later followed his example and used the Toltecs as a source of legitimacy.

In the mid to late 12th century the Toltec capital of Tula fell. Following this, other Central Mexican cities assumed the mantle of "Tollan" and the term eventually became synonymous with any big city in Mexico. Later, the Mixtecs would also use the moniker "place of reeds" to refer to the Aztec capital of Tenochtitlan as well. Cholula was one of these cities that was frequently referred to as Tollan. Now, I personally have not heard of the Mixtec kings appealing to Cholula specifically as a source of royal legitimacy. (I'm not doubting you - it's just new to me.) But, it would make sense in this context. Cholula could have been seen as the continuation of the Toltec authority that had been used as an external font of power since the Early Postclassic.

I realize this isn't a definitive answer, but its the best I could come up with. I have a book sitting on my bookshelf at home about the Mixtecs that could probably provide more context, but I'm in Mexico and didn't bring it with me. If you end up finding more information about this please let me know, as I'd love to hear more!