Supposedly, they could have changed the eqs for the badge, and this site will not have shown the updated reqs yet....Who knows, you may be the first to find out
But seriously... are you ABSOLUTELY CERTAIN you get 10 healing point in a round ? Looking at your stats you got at most 20 in a DAY. And you need 10 in a round.
Absolutely BEST way to get the healing points without padding is to join a VERY populated 64 player server. I got mine on Karkand, because this is where you will find the most inf, and healing people in cars is not feasible at least not for a total of 10 points. You need to run (or drive if need be) after the inf.
First thing to remember is that you can "only" throw 5 bags on the ground at any given time. Once you throw #6, #1 will dissapear. If you're NOT the only medic, this means that you shouldn't waste your time trying to throw all your bags in the same area unless this is the "only" area with heavy fighting. Also remember that you can heal people simply by holding the bag in your hands while being next to them, if you don't NEED to throw a bag, dont.
Second thing is to run after the inf. Notice where the fighting is. You need to stay VERY close to the fighting at all times. Switch to the med bag when you dont need the gun, someone might be running by who is only slightly injured. You will only see "missing health" on soldiers once they are at least halfway injured. If you notice an area where a machinegunner or assault is mowing down your people, drop a bag or two where their bodies landed, then revive them. They will probably get a few more hits and need one of your bags while running away to safety. Drop a bag more near this location for the next guy attempting to get by. Once the MG gunner has been neutralized, move on to the next choke point and do he same. STAY behind the assault people. You're their backup, not the frontline soldier in this scenario.
Third thing to notice is that ENEMIES can ALSO pick up your bags, and you get no points for healing them, so dont place them too close to the frontlines unless you have to.
Speific places to place bags are hard to define as this depends on your team, and what flags have been capped, and where the armor is. Generally, follow the flow of friendly soldiers and drop bags at choke points and flags.
If you're MEC dropping on spawn points will often yield SOME rewards, due to spawnraping, but in general you can only get one point from any one guy withint a certain timeframe. So dropping MORE than one bag that is picked up by the same guy because a G3 just opened up on him will NOT net you two points. While it's counter productive to the teamplay, you WILL get more healing points by dropping only ONE bag at each of the four MEC spawn points near the hotel flag (initially).
If you're US, dropping bags on the first street will at least get you one or two points from the nades flying through the air in the beginning. The same is usually true of the second street. Once the armor gets into play, you're pretty much going by luck. However, once the hotel flag is taken, the small confined area just north of the hotel flag (with the building you can enter) is usually a good place to place bags. On occasion MEC gets confined to the island and the US holds all flags west of the Train Accident. At this point in time close quaters battle is less likely to happen, and you can get MANY points from healing people from sniper fire and spash damage from the APCs, REGARDLESS if you're MEC or US.
Good luck.