Scrub that, I totally forgot that the Badges were used to determine rank.
Personally, 15 kills and fewer than 10 deaths is a really good goal but to decrease the need for someone to confirm it (be in game or see the footage) we could just use the Battlelog, look at their kills (it shows best gun and amount of kills) and deaths.
Therefore one easy screeshot or link to prove (as long as they used the same weapon for all the kills, and it was the weapon with the most kills for the person) and they get the Marksman Badge.
So yea, sorry about triple-posting.