繁体 or 简体， the grammar is the same
And yeah, there are also sentences that use 才刚，but that's a different meaning from 刚才。"刚才" is a word in itself; “才刚", to me, doesn't really fit that description, although it's totally fine to use the two words in that order with a different resulting meaning. You have a good point: "我才刚说了那一句话" is definitely different from "我刚才说了那一句话." The problem our students have, though, is overusage of 刚才, and this is aimed to help them realize when they need to use 刚 instead.
A lot of textbooks introduce 刚 and 刚才 together, but the only difference students have to go on are rough English translations. This video is trying to help students get beyond the English meaning & see how they are used differently. Really, we just want students to stop saying "我刚才从中国回来了“， which a lot of them say because the difference isn't so big in English.