The Corpsman could very well be holding the Marine's carbine. Not doubting that possibility. However it is well known and common for Docs to carry carbines in the Pacific.
Now we come to the 82nd. I have two sources from vets showing evidence of them carrying weapons.
Example A shows them being ordered to carry the M1911A1 on the Italy Jump. Source: Combat Jump by Ed Ruggero. This selection comes from page 168 and is based on an in interview with 505th medic Fred Morgan:
"As Sayre and his A Company troopers consolidated their gains and prepard to assault the winery, Morgan and his fellow medic prepped a strectcher for their wounded man. Sayre could not spare any riflemen to escort them. Although the Geneva Convention allowed them to carry pistols for self-defence, Morgan and his comrades did not. Instead, they wore white armbands ith a red cross that was supposed to keep them safe as noncombatants. (By the time of the Italy jump, in September 1943, the command ordered the medics to carry pistols. A Crate of .45-caliber automatics arrived at the departure airfield as Morgan was loading up, the weapons still thick with the cosmoline grease used for packing. Morgan traded his weapon with the Air Corps crew for cans of fruit. By the time of the fighting in Normandy, in 1944, a Morgan removed the white armband, which attracted attention, but he did not carry a sidearm during the war.)"
The next selection comes from B/508th vet Paul Demciak who jumped with the 508th Pathfinder team as the team medic. This is from the 508th Association website.
I was a pathfinder with the 508th P.I.R. 82nd Airborne Division. I jumped out of our C.47 Dakota Airplane before midnight on June 5th, 1044.
The mission of the pathfinders was to set up the Eureka panels. These were a canvas reflecting material and to light the beacons to mark the jump zones of the main force of paratroopers to follow in a few hours.
I and the others in the plane jumped west of Ste Mere Eglise and came under fire from German forces. Tracer rounds could be seen in the night sky and I prayed my parachute would not catch fire.
I did not have to worry because I jumped from a height of about 300 feet. It takes about 100 feet for a parachute to open. I looked up at my chute, and when I looked down I hit the ground.
I landed with a group of 9 men and officers under steady small arms fire.
While setting up the drop zone, the Germans threw grenades at our group. I was hit in the leg by shrapnel from a grenade while fighting off the enemy.
We were surrounded and I threw my carbine and trench knife in the woods and was taken prisoner. I was placed in a German truck with other P.O.W.'s north east of the River Douve, west of Ste Mere Eglise. The Germans were moving east in a convoy filled with American P.O.W.'s.
Just then, American fighter planes attacked the convoy. The convoy stopped, and the planes continued to shoot up the trucks. As the attack continued, everyone began to hurry out of the trucks. I was the last one out of my truck, and when I got near the tailgate, I was hit in the right shoulder. I fell to the ground and sustained a head injury.
After the attack ceased, the Germans marched us to Stalag 321 in Rennes, France where my wounds were treated.
After a few weeks we were forced marched 20 – 30 miles and placed in railroad boxcars.
For a week or two they were trying to get us to Germany.
Again American fighter planes attacked the boxcars, and I was hit in my right forearm. The wounded, including myself, were taken to a German hospital in Tours, France.
While there, the Germans wanted to amputate my arm. I jumped of the operating table and told the German doctor, "NO, NO, NO." The attending physician then made a wire ladder splint and wrapped my arm in white crepe paper.
After a few days we were marched south for about 600 miles to Touloise, France.
On September 2nd, 1944, I was in a German Hospital and on September 3rd, I and two other American P.O.W.'s heard gunshots in the hallway outside of the hospital room we were in. When we opened the door, we saw the French underground movement had shot the German Guards and threw [them] down the elevator shaft.
The P.O.W.'s all from different countrys were taken to the hospital basement and placed in 3 separate ambulances for transport to a warehouse outside of Toulouse.
On September 4th we met MI-5, English and American intelligence agents and officers in the French underground.
They informed us that 9 P.O.W.'s on the morning of 5-6 September will be sent by plane and taken to safety.
On September 6th, we were awakened at 4.am and taken to a grass field where the French underground had secured the area from the Germans. They had parked vehicles with small lights to guide the plane in.
The British Dakota plane was flown by a British crew. The plane landed safely.
We took off and I could hear the plane being hit by small arms fire.
A few hours later we landed in Naples, Italy.
While in the 118th Station Hospital, I was treated with a fluid diet and vitamins. I weighed 160 pounds when I jumped on D-Day, now 60 days later I weighed only 98 pounds.
On the forced march, we were not given any food and little water for 5-6 days. We were fed black bread, turnips and sugar beets whenever we got it.
The trench knife that I threw away in the woods was sent to my mother in 1946.
A French citizen found it with my name etched on the scabbard.