There are a couple reasons for the .300 magnum minimum suggestion by nilgai guides.

1) Many still "hunt" nilgai by chasing them with vehicles. The only reason I can figure they do this is because if many Texicans can't hunt something from a stand next to a corn-feeder, then they're baffled. Shooting at running nilgai results in a lot of misplaced shots.

2) Many Texican guides are used to deer and pigs, where "premium" bullets don't make nearly as much difference, so don't have a clue about why a "premium" bullet might work better on a larger animal. Hence they're fixated on the cartridge rather than the bullet.

If you HUNT nilgai, rather than chase them with vehicles, and use decent bullets they die pretty quickly with good shot placement. The hide is very thick over the shoulders and neck of big bulls, which is why premium bullets help, rather than deer and pig bullets. But I would be quite happy to hunt nilgai with a .270 Winchester or 7x57 with premium bullets, and maybe something even smaller, though unless somebody's extremely recoil-sensitive I don't see the point.

“Montana seems to me to be what a small boy would think Texas is like from hearing Texans.”
John Steinbeck