OK forgiving the non-PC correct term ‘manned’
Scenario: A decent stage malfunction sends their lander crashing to the martian surface. It is clear that they were alive when their lander hit the surface, then assumed that all died on impact, it could not be expected that anyone would survive and also it appeared the crew was working up to the point of impact to recover.
Do we give these people credit for being the first humans on mars? Can we say they were actually on mars?
I say they were on Mars regardless of whether they were alive for a fraction of a second or not.
Also the nation would be falling all over itself to memorialize the “heros” who went to Mars and basically grant them honorary Mars lander status.
The idea of a “first” is that you’ve done something successfully. Crashing and burning on the surface is not a success. It could be viewed as an accomplishment of sorts, but I think it’s reasonable to say that no one would be looking to repeat the experience.
I liken it to the English settlements in the 17th century.
Jamestown is known as the “First Permanent English” colony in the New World. Of course, there were other attempts:
I have no doubt an unsuccessful mission to Mars would be remembered as the first, but with an asterisk. The one more commonly remembered/celebrated would be the first successful mission.
Alcock and Brown, the British flying aces who were the first to fly across the Atlantic Ocean in 1919, are pretty much forgotten – by Americans, anyway – because they took off from far Eastern Canada and crashed in a bog in the west of Ireland.
More people remember Lindbergh because he did it solo in 1927, took the much classier route from New York to Paris, and, y’know, American.
I always thought Alcock and Brown were pretty cool. Made a special trip to the London Science Museum to see their re-built airplane, which is essentially an enormous gas tank with wings.
I’m firmly in the “who cares what the label is” camp. The label doesn’t in the least change the actions of those who made the attempt.
There is also some thread of evidence (or is it just urban legend?) that the first heavier-than-air flying machine was flown in March 1903, about nine months before the Wright Brothers, by one Richard Pearse in New Zealand – after whom our own pilot Doper Richard Pearse has eponymously named himself.
Wait a minute. I’m confused. You say, “It is clear that they were alive when their lander hit the surface, then assumed that all died on impact.”
So when they hit the surface, they died upon impact, yes?
Yes, they all perished during a unplanned emergency unsuccessful lithobraking ‘maneuver’ that also destroyed the landing craft as it hit the surface.
Yeah, they’re not just ON Mars, they’re ALL OVER IT.
And Gustave Whitehead did it two years earlier. . . Maybe. . . .
The lander hits the surface a split second before they hit the lander and go splat. 
On the other hand, didn’t folks sing the praises of Arrhichion?
Got a statue and everything! The champion who was never defeated at Olympia!
If someone tries to land on Mars in the next 50 years he’s not coming back alive even if he does survive the landing. So if he’s alive for even a nanosecond on Mars he’s the first man on Mars. The important event will come much later when someone returns to Earth after landing on Mars.
Did they get time to crawl out the wreckage and plant a flag before they died? No? Then it doesn’t count.
I think the real response in a situation like this would be a lot more nuanced than a simple yes or no. For example, even with a crash, you could still call them the first mission to Mars. For the second mission, you could call them the first people to set foot on Mars.
Overall, I’m in the no camp. A crash landing is not a successful landing and body parts do not constitute “first people on Mars.”
I’d say ‘yes.’ It reminds me of Michael Kearns, who was part of a four-man team to try to skydive to the South Pole. He was the only one who survived the jump.
From a ‘Washington Post’ story: https://www.washingtonpost.com/archive/lifestyle/1998/02/08/out-of-thin-air/907da7d6-b03d-40b3-9189-5cfb4790884d/
“I’m South Pole Five,” he says. Meaning, he is the fifth sky diver to land at the South Pole.
But wait – there was that Norwegian who solo-landed in 1992. He was the first. Wouldn’t that make you the second sky diver to land at the South Pole?
No, he says, quietly and precisely. The fifth.
This is the second mission to mars as in this scenario there was a (single) previous manned mission that did manage to fly thru the martian atmosphere, aborted back to orbit then back to earth due to insufficient fuel to assure a safe return and with some other associated problems - basically it was land on mars stranded or fly back home, the choice was to go home.