If there is a disagreement about whether meaning is always compositional in phrasal verbs, then simply put, it isn't. This isn't controversial - can you argue that idioms don't exist? Roidhrigh, do you disagree with this, or is your problem with the article something different? Do you think that there is too much emphasis on the concept of catenae or that statements about how they relate to meaning are too clear-cut and don't consider alternative theories of meaning? 

 Regarding the name of the article, the article suggests other names as well, like "compound verbs". The name is confusing because there isn't a phrase corresponding to a phrasal verb. 

 Can I suggest "A verbal idiom involving prepositional phrases and particles" as a definition? I'd also mention that particles have been categorized by some as prepositions.