That refers to the events of the evening of the 5th (and may not be all that correct anyway, don't rely on Thiers). The Macdonald quote was from the main battle on the 6th, sorry I didn't make that clear.I'm not saying that what happened was Bernadotte's fault, just that the account he gave in his proclamation was complete nonsense - even by Napoleon's low standards of veracity.
Yes, but Bernadotte's order of the day covers both days: "Saxons, during the fighting of the 5th July ..." And with regard to "The village of Deutsch-Wagram was not in our power during the day of the fifth" - no, because Bernadotte's Saxons, on the verge of taking said village, were set upon from the rear by MacD's men, who then fled in a panic when the Saxons returned fire. So what MacD says about the 6th is only partly germane, even if we did not have reason to believe MacD's account was designed primarily to make himself look good. (Which we do.)
Bernadotte's order of the day was intended simply to boost the morale of the Saxons, no doubt somewhat shaken after being attacked from behind by MacD's men while they (the Saxons) were close to defeating the Austrians. His order is all about the courage they had shown fighting bravely for NB, and says nothing of himself, by the way.
Perhaps the most telling sentence in these two very contrasting orders is "His Majesty owes the success of his arms to the French troops and not to any foreigner." Ah yes - NB the broadminded visionary of a united Europe. LOLOLOLOL, as they say.