Both are possible. 'At' is more likely, in my opinion.
Can being at the railway station be understood as being near it?
Cf: The teacher is at the chalkboard. = The teacher is near the chalkboard.
If the teacher is at the chalkboard, then I expect the teacher to be standing right in front of it, probably in the act of writing on it or pointing at words already written on it.
'Standing at the train' is an unlikely phrase.Should the preposition "at" be considered here as a preposition of place implying a certain adequate action, but not just a conventional preposition of place?
No.
Thus, "standing at the train" means not just "standing near it", but suggests some actions (e.g. checking up the tickets or repairing the carriage etc.)
'Standing at the train' is an unlikely phrase.
Still the question remains. What about such "likely" phrases as "to be at school, to be at the office, to be at home, etc.)? Does the preposition at implies not only just being inside but also being engaged in doing sth?
e.g.
He is at school therefore he is not only inside the building but is also having classes or is being engaged in some specific activity connected with his schooling.
Should the preposition "at" be considered here as a preposition of place implying a certain adequate action, but not just a conventional preposition of place?
Thus, "standing at the train" means not just "standing near it", but suggests some actions (e.g. checking up the tickets or repairing the carriage etc.)
:up:Yes, there are some where adding or omitting the article makes a difference. In BrE:
He is at school = He is engaged in educational activities somewhere on the grounds of the school he attends.
He is at the school = He is probably inside the building but we don't know what "he" is doing. He might be a teacher, a pupil, a builder, a visitor, a school inspector ...
He is at work = He is at his place of occupation doing whatever it is he is paid to do.
He is at the office = He is probably working, but this could simply mean he has popped into his office at 10pm to collect a jacket he left behind earlier
He is at home = He is in his own place of residence. It tells nothing else.
He is at his parents' home = He is at the house owned by his parents. If the family are together then his parents are at home, and he is at their home.
Yes, there are some where adding or omitting the article makes a difference. In BrE:
He is at school = He is engaged in educational activities somewhere on the grounds of the school he attends.
He is at the school = He is probably inside the building but we don't know what "he" is doing. He might be a teacher, a pupil, a builder, a visitor, a school inspector ...
He is at work = He is at his place of occupation doing whatever it is he is paid to do.
He is at the office = He is probably working, but this could simply mean he has popped into his office at 10pm to collect a jacket he left behind earlier
He is at home = He is in his own place of residence. It tells nothing else.
He is at his parents' home = He is at the house owned by his parents. If the family are together then his parents are at home, and he is at their home.