That sentence is not incorrect.
The list of allowed modal brauchen-forms should contain, besides negated phrases, nur-phrases as well.
nicht zu tun brauchen = need not do. (Du brauchst das nicht zu tun.)
nur zu tun brauchen = must/need only (to) do. (Du brauchst nur xyz zu tun.)
A common application of the nur-phrase is when you don't know how to do something and somebody tells you how simple it actually is. (Das ist gar nicht so schwer; du brauchst nur den roten Knopf zu drücken und schon funktioniert's.) To some degree, the structure "du brauchst nur X zu tun und schon passiert Y" including the second "und schon"-part is a fixed idiom.
Another application: When there is a list of tasks to do and you are told only to do part of if. (Du brauchst nur die Nudeln zu kochen, die Sauce brauchst du nicht zu kochen.) Depending on the context, it is forbidden to do the rest as well (You need only to cook the pasta. But do not cook the sauce!) or it is simply not required (You need only to cook the pasta. But if you want to do me a favour you could cook the sauce as well.).
The comic is somewhat tricky regarding the use of "brauchen". A says "Wir sollten herausfinden, was sie brauchen, und es ihnen geben." Here brauchen is used non-modal. This implies that there is a (mental) list of things that the customers need.
B takes this list and interprets it as a list of things that the customers need to do. (This can be seen from the modal usage of brauchen). By saying "Sie brauchen nur unsere Produkte zu kaufen.", he reduces this list to the only relevant task: Buying the company's products.
The transformation between "list of things that customers need" and "list of things that customers need to do" is of course not explicitly mentioned and is part of the pun.