No, that's a common misconception.
Vinegar was part of the "daily issue". Regulation said that every man would receive 47ml of vinegar. The sergeant of each group would carry to 2 canteens. One for himself with water, one with vinegar for his troops.
All of the above is the exact same you said, but here comes the difference.
Vinegar was only issued by the Generals orders and only during hot summer days. After 1797 it was only issued if there was an order from the commanding medical officers. It was not meant to keep the cantees from rusting or making it taste better, it was meant to let the water spoil slower by preventing bacteria inside the stale water to spread.
Same actually goes with wine. Wine was issued. But only on the generals orders. After 1797 it was issued to troops on forced marches, heavy working duty, on battle days and always for troops in besieged cities.
Troops in besieged cities received 230ml wine and troops on the front/in the field received 150ml wine. From 1801 on, both troops in besieged cities and troops in the field received 250ml wine.
This rusty little piece of shit is one of mine.
I bet it is very sanitary. It is made out of lead and rusts like crazy... As you can see.
But hey! Its accurate!
Die of lead poisoning and get the 'Ultimate Reenactor' achievement
I actually lined it with beeswax which works pretty well. Some parts are not covered, but overall it keeps it from getting into the water. Also on a plus side, on hot days, my water tastes like beeswax which is a nice taste compared to the taste of cold water. (not)