It is always best to go back to the source being referred to and not rely on an interpretation in a book review that may or may not be accurate.
What Broers wrote on page 84 of his biography, following the citation of what Napoleon wrote to Dupin, Adjoint to the Minister of War in Paris is:
'The young officer had not the slightest hesitation in lying in extremis even to the Ministry of War. The British had sunk twelve French warships in Toulon and made off with another twelve; they had burned all the timber stocks needed for repairs and construction, carefully accumulated under the monarchy. Philip Dwyer has placed these losses to the French navy in their full perspective by recalling that the were greater than those Nelson would inflict at the Battle of the Nile. Letizia had always chastised Napoleon's habit of lying, to no avail, and as his wars progressed a waggish expression took root in France, 'to lie like an army bulletin'. The above may well be the first such example...'
So Broers' comment regarding the later bulletins and Napoleon's letter to Dupin is conditional, not definitive. That is a significant difference.
It would also have been better, to my mind, if Broers had not used or referred to Dwyer, but that is merely a matter of opinion on my part.
The quoted letter to Dupin on the same page of Broers is:
'I have told you of this brilliant success...it is enough for me to tell you that the English have not captured one of our guns...The enemy has been thrown into the most unheralded retreat...They did not even have time to set fire to their ships...They have not burned our stores of wood or rope. I have visited the naval arsenal, and I can assure you that even the worst they have done to us is reparable.