Some parts of the story may be exaggerated or uncertain. For example, a couple of researchers at the Field Museum in Chicago did a study of contemporary sources and say that the number of dead may be exaggerated. Patterson himself made conflicting claims on that, from 14 to 135. The Field Museum researchers think it may have been 28.

That doesn't mean Patterson necessarily lied. Part of the problem was accurate record keeping. They kept good counts of the dead Indians, but there were no accurate counts of the number of dead Africans. And it's hard to establish whether kills in neighboring villages were made by the same lions or different lions. As they point out, man-eating lions were a constant presence in that area, having killed people long before the Tsavo lions appeared, and continued killing people until WWI, long after the Tsavo lions were dead. The Tsavo man-eaters weren't the only man-eaters around.

However, even the high numbers like 135 are not crazy high for man-eaters, though they may be inaccurate for the Tsavo lions. The Champawat tiger in India/Nepal killed over 400 people, and its kills are well-documented in newspapers and public records of the time. The Rudraprayag leopard in India killed over 125 people.

Specific details of what Patterson did can't always be independently corroborated outside his own writings. The story of the trap you mentions is among them. But I wouldn't pass it off as incredibly unlikely.

First, the details of the trap are very sketchy in Patterson's account. He mentions fashioning it out of railway sleepers (the wooden slabs on which rails are laid), rails and chain. We see someone's imaginary view of what it might have looked like in the Val Kilmer movie, where it looks pretty solid and sophisticated. But nothing Patterson actually says describes it in that much detail, and if you look at what he does say (such as shooting holes in rails with his rifle because he had no drill), it appears that it was very crudely made, and may not have afforded as much protection to the men as you might think. Then there is weird stuff like putting the lights (the lanterns) on the human side of the trap rather than the lion side. If you want to shoot something, you should arrange lights to illuminate the target rather than arranging them to blind yourself in the dark.

So it's not surprising to me that a couple of guys sitting alone in the night behind a precarious barrier might shoot poorly at a known man-killer on the other side. How much light was there to shoot by, how many lanterns? Were these good lanterns or smoke dulled crappy lanterns? Were the two guys even trained to shoot? A lot of "sepoys" were people who'd never handled a gun, or were given token training on some ancient blunderbuss. Did they take such people and give them a couple modern rifles just for this occasion? So many details are missing.

Even the best of shooters may be confused in the semi-dark with a man eater raging behind a "wall" of hanging railway sleepers and odd bits of chain. The story does say they found some blood on the other side, so they didn't miss the lion entirely, they wounded it.

I don't think we can dismiss the story over the trap account. He may be wrong about the number of people killed by the tigers, but that's a matter of guesswork on everyone's part, he had no way of knowing exact numbers.