Harry was sat at the far end of the seventh years, closest to the Staff Table.(This usage is commonly heard in Britain, so I'll use examples from Harry Potter.)
There are two problems with this usage of "sat." The first is that the construction sounds passive, as if Hagrid had picked Harry up and plopped him down in place. The second is that "sat" is the simple past tense of the verb "to sit," not a participle. Correct ways to express the meaning of above sentence include:
Harry sat at the far end of the seventh years, closest to the Staff Table.
Harry was sitting at the far end of the seventh years, closest to the Staff Table.
Harry was seated at the far end of the seventh years, closest to the Staff Table.
If you do want the passive, the correct verb to use in this case is the transitive verb "to seat."
The maitre d' must have recognized Ron and Hermione's first-date nervousness, because they were seated in a quiet, dark booth in the corner.
The same holds true for "was/is stood": the correct usage is "stood" or "is/was standing."
Does this mean you should never, ever use these constructions in your writing? As always, character makes a difference. The usages "was/is sat" and "was/is stood" are common among some in northern England. Professor Snape would never deign to let his working-class roots show by speaking in dialect, but his Muggle father very well might.
Tobias jabbed his finger at his son. "When I get back, you'll be sat there quiet as a mouse, if you know what's good for you!"