Crevier was indeed well versed in Roman history:
The author is not always happy in the choice of details, and his style, diffuse and without grace; offers only too many Latinisms; but the critic should have noticed the order and the sequence of facts, wise reflections, virtuous feelings, and above all put forward the advantage that the author drew from the ungrateful materials that he had to use. Indeed, if he is supported by Tacitus in the history of the first Caesars, he soon has no other guides than the writers without criticism and without talent who composed the History of Augustus.
This edition, enriched with judicious and learned notes, and preceded by an ingenious preface and perhaps too oratorical, but always elegant, was appreciated by foreign scholars, who spoke of it only with the greatest esteem.
Thus, it is his translation which was very often used as a reference to measure later ones against. Despite him often imitating the original author and using Latinisms where they would be inappropriate today.
In case of these supplements, it is at the peril of internet textual databases, that they do not preserve the original layout.
Crevier is the author of these passages, to make missing source material connect to what was left in writing to him. In real books this is made explicit:
This book is very imperfect; a great part of the beginning of it is lost; and there are, besides, considerable chasms in other parts of it. The supplemental passages which the translator has introduced, to complete the connexion, are taken from Crevier. They are printed in a different character.
— Daniel Spillan, Cyrus R. Edmonds, William Alexander McDevitte (translators): "Livy, The History of Rome, Volume 4", Bohn's classical library, Bell: Rome, 1890. p1915