I'm pretty sure that CBS themselves had full episodes posted on YouTube, at some point within the past few years or decade, but they seem to have reversed course on that.
You and EnsignTOS are correct; simply visiting the page where the episodes were posted would make it perfectly obvious they were legit:
https://www.youtube.com/channel/SWZk2dX5DnW_c
The clips that are there now were always present and would be just as much of a copyright violation as the full episodes. The episodes have been up for only the last few months and just came down in the last week; I know because I used to play them on my iPad as I nodded off to sleep. =(
The episodes were the 1985 transfers (i.e. not TOS-R) and strangely several episodes were missing (I Mudd, A Private Little War, Assignment: Earth, ...And The Children Shall Lead). CBS probably felt comfortable posting them on YouTube since they were not TOS-R, only 360P, and could not be downloaded. They apparently had second thoughts for whatever reason.