The relation between cattle ranchers and indigenous peoples is... spotty, and incomplete. As you suggest, the biggest fights were generally with government troops, not with random cattle ranchers. There were also occasionally fights with towns and their citizenry, particularly when raiders reached these areas. The nations particularly known for their raids at the time included the Karankawa (up to Texan independence), the Comanche, the Apache, and the Kiowa.

But that still doesn't really explain the trope, because it doesn't mention cattle ranchers. Well, it might help if I said that raids generally weren't just wanton violence (except in the case of retaliation attacks, where wanton violence was committed against them first), but instead to capture goods. Of these, livestock was highly valued, because it was not only a fairly productive enterprise in terms of both money and meat or wool/hair, but because, well, there was an awful lot of it, and it was pretty easy to sneak in and take a few. This was one of the main concerns of the cattle ranchers ie cowboys during the classic Wild West timeframe (C. 1865-1885~1900)

Cattle drives were a long, difficult, and dangerous affair. These men (and some women) were basically sailors of the land: they'd go out in very poor living conditions for a few months in almost complete isolation, often eating cheap jerky, canned beans, and watered-down coffee for the entire trip. Their drowned out the troubles, much like sailors did, by drinking, whoring, and all-around troublemaking when they finally got to their destination towns, for which reason people didn't like them very much. These cowpokes often carried guns for self-defense against rustlers and indigenous peoples, though in both cases livestock theft was typically done quietly and often by night, so actual gunfights for this wouldn't be all that common.

Now, there is another point to address: cattle drives often passed right through "Indian Country". You'd think this would increase the risk, but... well, it didn't. While it's true that certain indigenous cultures with a particularly density in the Texas area had developed raiding cultures, by and large these were still just people who were just as interested in peaceful interactions as anyone else. Not just that, though, but they were often in difficult conditions due to their treatment by the US government, forbidden from leaving their reservations and issued less than enough food to really last. Many cowpokes who saw this, rather than antagonistic, were actually highly sympathetic!

One anonymous cowboy wrote:

"The people we saw, scattered about in small villages or begging [beef] from us, were not the 'savage foes' of Western lore but a sorry lot of starving human beings. We met an old scout called Amos Chapman, who acted as interpreter for the Cheyenne. He said their people were getting beef, cornmeal, flour, sugar, but no beans, rice, hard bread, or salt. Rations are issued for seven days but last only three. After months of pleading with the government agent, Cheyenne braves were allowed to go on a buffalo hunt, where they found nothing but bones left by white hunters"

This might seem a shockingly sympathetic account for groups depicted by Hollywood as inherently opposed, but ranchers generally didn't even come across any indigenous groups on their trails, despite running right through Indian Country. That's because the trails were pretty regular, and more importantly, the Great Plains are huuuuuuuge. Even with nomadic nations, the odds of a chance encounter are fairly small. On top of that, if they really wanted to rustle some livestock anyway, they had easier targets to pick from, including other indigenous peoples, some of whom (like the Navajo) had picked up their own ranching practices in the centuries since contact with Europeans, and who also raised livestock other than cattle which would've been much more useful to steal for them.

See, that's a good point. Cattle are a difficult thing to deal with. They're big, most indigenous Americans are/were lactose intolerant, and especially if you don't have any salt then the meat can go bad pretty quickly. They have their uses for the enterprising Plains rider, such as leather crafting and the like, but compare this with sheep and goats whose hair can be used to make not just tarps for dwellings, but also rugs, clothes, saddles, pretty much everything that leather could be used for and some on the side. They're also easier to keep around, and in larger numbers, so leathers and meat can be more accessible in general if you have them. Cows, by comparison, are a difficult target - they're worth a lot of money, but from a practical standpoint they're also more difficult to work with, and the cultural significance of the buffalo/bison could probably outweigh what they could get from cattle even if we disregard the fact that buffalo are also significantly larger and thus give more of everything anyway, so if you're taking on that burden you might as well go big if the chance presents itself.

So, for a variety of practical and diplomatic reasons, cattle ranchers and indigenous peoples rarely fought. The groups rarely met, and when they did, it tended to evoke sympathy rather than suspicion or violence - perhaps because the ranchers got to see their plight firsthand. Although raids and battles did take place, it was usually against easy targets, or national military forces of the US and Mexico, or otherwise against posses, but generally not ranchers. When rustling did happen, it was usually quiet, and the point of that was avoiding armed conflict as much as possible. Ranchers had more conflict with their fellow Euro-Americans, who as townsfolk despised them for their rowdy, unruly, and violent behavior, as rustlers had access to the same markets that the ranchers were using unlike indigenous peoples, and as a government inflicted a severe plight upon the indigenous nations that the ranchers found miserable and inhumane.

Perhaps the last "Indian cowboy" fight for an example would have been when in 1911 a family of 12 Shoshone killed some cattle for food and hung parts of the meat up in trees to freeze it through the winter for food. A herder witnessed the event, and a posse was formed to hunt them down eventually resulting in a two-week search and a three-hour fight. When the smoke cleared, eight of the twelve were killed.

One posse member was killed, and the "cowboy/Indian" type of conflict was over. That happened to have been the last time when ranchers fought Indians, but there could well have been others. In Texas history, there were many fights between the Texas Rangers and local ranchers and raiding Comanches in particular to steal horses.