In most languages, obviously, closing quotes and parentheses is necessary. There are some who think their elision in TI-BASIC leads to bad style, and some who think it's more elegant to leave them off.
When I regularly used only TI-BASIC, I was of the latter opinion; it doesn't make sense to add close-quotes for clarity when the line ends everything; in fact, lots of closing parentheses make the end of the line harder to read. Then I started learning Java, Python, etc; and now Scheme, and I make errors by forgetting closing parentheses or misplacing them once in a while. My carelessness don't speak for everyone, but I'd say that, if TI-BASIC were in a vacuum, it would be better not to close parentheses, while in the real world the clarity doesn't really offer a net benefit.
In optimized code, it's trivial to remove the closing delimiters, and this provides, in most cases, an equally trivial advantage. Most people learning TI-BASIC don't want to, and shouldn't, micro-optimize everything they write.
The other issue is consistency; but the tutorials here are inconsistent anyway. So I don't think that should influence the decision.
