The quote appears to be accurate. Pope Gregory VII agreed with those who felt that Latin was a sacred language and were suspicious of change. He therefore tried to stop the circulation of the Slovenic version called for 200 years earlier.
His actual reason for trying to stop it is clear within the statement. Lay people were often quite uneducated at the time. There was a legitimate concern that some of these people would have significant trouble interpreting the Scriptures for themselves.
Even today the same concern was addressed in the document Dei Verbum:
“It devolves on sacred bishops “who have the apostolic teaching”(7) to give the faithful entrusted to them suitable instruction in the right use of the divine books, especially the New Testament and above all the Gospels. This can be done through translations of the sacred texts, which are to be provided with the necessary and really adequate explanations so that the children of the Church may safely and profitably become conversant with the Sacred Scriptures and be penetrated with their spirit.”
Notice the emphasis on instruction and explanations. And the reason: So that the children of the Lord may SAFELY and PROFITABLY come to know the scripture.
The Catechism lays out these principles:
V. SACRED SCRIPTURE IN THE LIFE OF THE CHURCH
131 "And such is the force and power of the Word of God that it can serve the Church as her support and vigor, and the children of the Church as strength for their faith, food for the soul, and a pure and lasting fount of spiritual life."109 Hence "access to Sacred Scripture ought to be open wide to the Christian faithful."110
132 "Therefore, the study of the sacred page should be the very soul of sacred theology. The ministry of the Word, too - pastoral preaching, catechetics and all forms of Christian instruction, among which the liturgical homily should hold pride of place - is healthily nourished and thrives in holiness through the Word of Scripture."111
133 The Church "forcefully and specifically exhorts all the Christian faithful. . . to learn the surpassing knowledge of Jesus Christ, by frequent reading of the divine Scriptures. Ignorance of the Scriptures is ignorance of Christ.112
The Church at the time of Gregory VII was concerned with the authority of the Pope. Because of the Church’s ties with the State and royalty the position had lost prestige. As leader of the Church this made the Pope somewhat impotent since quite often the people looked to their rulers on religious matters. Gregory was attempting to regain the importance of the papacy which it had lost. He wished for the laity to rely on the Church for guidance. Maintaining the traditional Latin translation would help in this cause.
Additionally, the Church had been dealing with many heresies. There was a legitimate fear that the unprepared people reading the Bible could fall into heresy through false interpretation of the scripture. Thus, it was his determination to keep the more “secret” Latin which had to be interpreted by the Church.