I can think of two reasons why people would say to pay out of pocket.
1) Via Napoli has had multiple reports of being sticklers for people on the dining plan not sharing their meals. Paying out of pocket, they don't care if you share. So if you are planing on sharing, everyone should be on the dining plan and using a credit.
2) The mezzo pizza is large and feeds 3-5 people, and costs $39. If three people split that, that is $13 per person. This is a pretty good deal in Disney (for really good pizza), so you don't have to look very hard to get a significantly more expensive entree elsewhere on the dining plan.
That being said, if you do want to use your dining plan, Via Napoli does allow you to use it - I believe if you are getting pizza you can get an individual pizza (though there might be a limitation on toppings if you do the "create your own" option). This may be a better option if nobody wants to share a larger pizza or if they would rather have an entree that is not pizza.