Yes, we may say that. More of an explanation though, like in response to "why is the shirt sweaty?" It wouldn't really be used as a comment without context. (Like if some just walks into the room and announces that they "run in the shirt". That would be odd. They could announce that they run in "this" shirt though.)
I hear what you are dsying but have to disagree a bit. I can see someone answering, "Because I was running," when asked why their shirt is sweaty. I'm sure there is a situation out there somewhere in which this response is warranted, but it certainly wouldn't be common. I run in a shirt would be much more common. Ultimately, it doesn't really matter; Duo gives us sentences that don't fit the mold to help us further grasp the language.
I did not mean to imply that it would be a common sentence/reply. I mainly just meant that it isn't a "clumsy yet grammatically correct" sentence like we sometimes see here. More to help the non-native English speakers with their English than anything else, per PaoloArman2's request.
Can someone explain this to me please? Hemd is neuter (das Hemd). And "in" is a "two-way" preposition. If the sentence is aktiv it takes the Akkusativ form. Since they are running, that seems aktiv. Achso, das Hemd...In das Hemd...Ins Hemd. I don't understand why it is Im Hemd. :O