In reviewing this material, I'm persuaded that, yes, there's more supposition than fact here. As will be described below, I think the matter still merits an endnote. But only as a hypothesis, and one that also should be flagged as such.
As Oxford's first biographer, B.M. Ward first pointed out, there's a record in the calendar of manuscripts at Hatfield House (XIII, 362) of a copy of a New Testament which is no longer extant. But the manuscript calendar does transcribe a Latin inscription from the book's flyleaf. Nina Green's excellent Oxford-Shakespeare website has the full Latin transcript with an English translation here.
The Latin poem from the New Testament's flyleaf contains homophonic, though not etymological, puns on Vere and the Latin veritas (truth). Here's part of it:
"[S]ince thou, a Vere, art wife and mother of a Vere daughter, and seeing that thou mayest with good hope look forward to being mother of an heir of the Veres, may thy mind always glow with love of the truth, and may thy true motto be Ever Lover of the Truth. And that thou mayest the better attain to this, pray to the Author of all Truth that His Word may teach thee; that His Spirit may nourish thy inner life, so that, thus alleviating the absent longings of thy dear husband, thou, a Vere, mayest be called the true glory of thy husband. ... To the illustrious Lady Anne Vere, Countess of Oxford, while her noble husband, Edward Vere, Earl of Oxford, was travelling in foreign parts."
Not exactly Virgil. Still, despite its anonymous nature, the context of the poem does suggest Oxford's hand, especially as it might offer an interesting glimpse into an insecure, doting zealotry in Oxford's intense scrutiny over Anne's pregnancy.