It must be that in the context of their writing, these words had a valid sense. In order for this to be true, it must have been plausible that one might rank the Baptist too highly vis-a-vis Jesus. As part of the set of Baptist/Dominical comparative logia, this reflects a dialogue between two schools of followers rather than reporting actual interaction between the individuals. As others have observed, this dialogue is in the gospel record conciliatory, and in no way vituperitive (as with the Pharisees for example). It is clear that Jesus inherited the mantle of the Baptist as the wilderness preacher of the kingdom of God. It is accepted that among Jesus' close circle of followers were former followers of the Baptist. What becomes less clear is the degree to which some Baptist followers remained separated from this trend, what might have motivated this loyalism, and whether later conciliations occurred.
No indications exist of any kind of hostile rivalry. The encounter with Gentile believers who knew "only the baptism of John" in Antioch would place Baptist followers in the diaspora. Their presence there indicates some kind of baptist mission. This mission may be parallel with, or even prior to the Christian mission. If it were later, it would not escape the role of a rival. Even as a contemporaneous event the sense of rivalry would seem unavoidable. But if it was indeed an antecedent, the role of "making straight the path" which John fulfills to Christian doctrine could be seen as passing over to the baptist followers in the diaspora as well. They only need a supplementary initiation and not conversion of any kind.
Any teaching which originates with Jesus or with the original circle of followers who were together since "the time of John" would be conscious of this continuum. It is with Paul that we find a faith that is divorced from this history. Paul, who counts knowledge of Jesus "after the flesh" as nothing would presumeably count knowledge of the Baptist as even less relevant.