The fundamental problem is that the descriptions aren't consistent. There are those the specify "any order" and those that don't. If they don't say any order then the tendency in a case like this is to interpret it as being literal "shoot T1 then reload then shoot T3".
As to T1-T3 meaning shoot them in T1,T2,T3 order, I've never seen or heard that interpretation before. But since it does seem to exist, that's even more of a reason to expand the stage descriptions.
The ones that specify any order don't need to. I included the ruled pertaining to classifiers already. As far as I know there aren't any that mandate a specific order,(T1 then T2, then T3, etc.) I don't think they can per the rules. It's very specific under the freestyle rules what classifiers are allowed to require.
The rulebook is there so that every single thing doesn't have to be written in to a stage description/briefing, although Troy already said he would work on cleaning them up some, that is very different from "expanding" them.