I don't believe that "The Gospel of the Lord" is stated at all for a passion reading.

The OP is correct, forthe Novus Ordo/post-conciliar liturgical rites.

While the greeting and signing are omitted, "The Gospel of the Lord" IS said or sung.

From the Passion Gospel book (which is a liturgical book in its own right), n. 8:

"At the conclusion, the deacon who is the narrator says "The Gospel of the Lord" and all respond "Praise to you Lord Jesus Christ". The book of the Passion is not kissed....."
"Cantu Passionis expleto, diaconus qui partem historici habuit, profert: Verbum Domini, et omnes acclamant: Laus tibi, Christe. Liber Passionis a nemine osculatur....."

Similarly, the Ceremonial of Bishops n. 273:

"....At the end the words are said, but the book is not kissed."

And from the Lectionary for Mass/Book of the Gospels, rubric before the Passion Gospel:

"The Passion begins directly without the greeting or acclamation of the people but concludes in the usual manner"

chonak, not for a while (given that the current US lectionary is a decade old) and the Ceremonial and the Passion Book date from the late 1980s.

My guess as to why people think the conclusion is omitted is as follows:
(a) Simple parallelism: since the introductions, greetings, signing, kissing (i.e. the typical "gospel" features) are omitted, people naturally suppose the same about the conclusion.

(b) Lectionary errors: in many early US lectionaries (such as the ones printed in the 70s), the Passion text (which was not divided) was printed with an error in the Passion readings of Palm Sunday (but not Good Friday, which was printed correctly):
-- the long version of the Passion began with "The Passion of our Lord....." but did not contain "This is the gospel of the Lord" at the end.
-- the short version of the Passion began with "+ A reading from the holy gospel...." and concluded with "This is the gospel of the Lord".
If people were familiar with these books, they would have naturally assumed that when doing the long version of the Passion, the typical "gospel" features were removed.

Hello there, In traditional parishes, where we use St Pie V rit, the Cantus Passionis is not preceded or followed by anything.
And most of all, until 1955 (the year Pie XII made a reform in the hebdomadae sanctae), the cantus passionis was divided in two parts, and only the breve, second one was considered as the Gospel.
"Schütz does set a choral 'Laus tibi' paraphrase, but it seems odd to me that Lassus, Victoria &c passed up their chance."
Of course, Schütz being protestant, this did not applied to him !
But for Victoria and Lassus, there is nothing because there was nothing before Vatican II.

Thanks to PLTT for the details he adds. The omission of "The Gospel of the Lord" also was carried over from the Lectionary to other books. My mid-1970s hand missal in English shows "This is the Gospel of the Lord" after most Gospel readings, but not after the Passions of Palm Sunday.

Another data point: the four-volume "Missale Romanum cum Lectionibus", published in 1977, shows "Verbum Domini" after all of the Passion gospels of Palm Sunday, both long and short versions, for years A, B, and C, and also for the Gospel on Good Friday