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The men gathered to leave before the Serbs got to the city and there was any battle. A soldier interviewed in St. Louis, Missouri where many Srebrenica families were/are settled, tells of getting the order for men to leave their defenses and meet at a certain place. He said: "There were strong points, strong defenses all around." Further, he says the problems/fighting with the Serbs began once they crossed into Serb territory - so the men were all out of Srebrenica. They were several thousands of Muslim men (including army men) streaming through Serb territory:

After the Fall: Srebrenica Survivors in St. Louis

P. 120 “Srebrenica Survivors in St. Louis: After the Fall” text and interviews by Patrick McCarthy: Quoting Hamil Becirovic – a soldier who walked out:

Srebrenica’s fall was very sudden. We were in our village when the attack began. There were strong points, strong defenses all around. My brother was with me. My mother, wife, and child were together and they went to Potocari.
Around 7:30 in the evening, we got the news that women and children should go in one direction and that men should go in another direction because of the possibility of attack.
The order came from the brigade commander in Srebrenica and the people followed that direction.
It was really hard. My wife took our child and left. I stayed behind at our house and waited for others who were leaving, so that we could go together.
About 11:15 p.m., the men started to get together and we went to a nearby village where the men were also gathering. I was with my family, friends, and neighbors. At one point, there were, I think, something like eighteen thousand men together in that one place.
They told us it would be difficult to walk from the place where we had gathered, to walk to Tuzla, because it was hard to organize eighteen thousand people into one row so that they would go one after another.
People started leaving about 1:00 a.m. It wasn’t our time to go until about 6:00 a.m. Those ahead of us were moving for five hours and we still didn’t leave until 6:00 a.m. – my brother and the others I was with.
We crossed the Serb line and it immediately became more difficult because we were in their territory. There was one huge group of people walking in front of us, marking the way to go. Of course, after eighteen thousand people go, there is a mark of the way, there was a trail of the way out.
…
I arrived in Tuzla on the seventh day.

I underlined the one part because he first says "when the attack began" but then says they were preparing to evacuate "because of the possibility of attack" - so it doesn't appear any real fighting has begun - and for him at least - he didn't mention his unit/section receiving or returning any fire when they got the order to leave their defense positions.

Seems obvious, that when the command removes a large, strong army with good defenses, which hasn't even just lost a fight to outside forces, there was purposeful planning to allow the city to "fall".