Cuttbows are not protected. Only fish that have been verified to some level of genetic purity as cutthroats are. In most cases, these pure fish are found only above some natural or artificial barrier that prevents nonnative fish from moving upstream, and so are the only fish you will find in the waters where you can catch them. Most these waters are closed to fishing, but some are catch and release, and this should be noted in the fishing regulations. In some cases, the fishing regulations are not explicit enough to know. For instance, where a stream has a barrier one mile up, cutthroats only above the barrier, and a mixture of trout below, the regulations may only say: "All cutthroat trout must be released unharmed immediately" or something like that. In these cases, you do find pure natives below the falls, as some fish move downstream. These fish are technically protected, but this is where the gray area is. Most of the pure populations are kept that way due to isolation above barriers and to either no fishing or C&R regulations. It is largely understood that some of these fish will move downstream, and may be harvested unknowingly by anglers (technically illegal).
The DOW also doesn't put signs in many places, because there are those who would sabbotage their greenback restoration efforts by killing the native fish or by introducing nonnative trout. Not everyone appreciates our native fish heritage. Some just want to catch and keep fish everywhere possible.
One of my favorite greenack streams is packed with thousands of fish, but none of the anglers I have ever run into have known that EVERY fish they catch there is a greenback cutthroat. Even when they know they are cutthroats, they are surprised to learn they are greenbacks. Because the regulations say merely that they must release all cutthroat trout, and there are no informational signs, many fish are harvested illegally, there. Fortunately, the population is large, so it can take a little bit of such pressure, but I still don't like to see the harvest.
It looks as though Greenbacks will be considered for delisting in the coming decade, and if delisted the state will have more freedom to manage them and will probably begin to allow some harvest.