How to prove Paul did not write certain New Testament books

In studying Titus 3:3-8 I came across this fine example of exegetical haberdashery from Raymond F. Collins[1]:

“Works of righteousness” (ergon ton en dikaiosyne) has a Pauline ring, but the apostle did not actually use the phrase “in righteousness” (en dikaiosyne). Writing about righteousness or justification, Paul occasionally used a prepositional phrase that includes “righteousness” as the object of the preposition, but the preposition is either eis, “in,”…or dia, “through,” “on account of”… The prepositional phrase used by the Pastor is, however, found in four pseudepigraphic epistles all influenced in some degree by the writings of Paul (Titus 3:5; 2 Tim. 3:16; Eph. 4:24; 2 Pet. 1:1; . . .

By way of explanation, Collins refers to the author of Titus as “the Pastor” since Paul-obviously!- did not write it. And note the unassailable logic that is used to demonstrate that Paul did not write Titus: “We know Paul did not write Titus because the author uses the same phrase found in other books that Paul did not write- Ephesians and 2 Timothy.” Ah yes. Well of course.

I believe this is what is called “begging the question.”

And the poverty is noteworthy.

In contrast to Collins, Donald Guthrie[2] comments of the same passage:

The negative statement not by works of righteousness which we have done is intended to bring out by way on contrast the absolute character of the divine mercy in the next phrase. RSV has a better rendering of the Greek, ‘not because of deeds done by us in righteousness’. The word dikaiosune (righteousness) here denotes observance to the Mosaic Law, in complete agreement with Paul’s general usage.

[1] Raymond F. Collins, I & II Timothy and Titus (Louisville: Westminster John Knox Press, 2002), 363.

[2] Donald Guthrie, The Pastoral Epistles (Grand Rapids: William B. Eerdmans Publishing Co., 1984), 204.