I would imagine it would take the vehicle sitting in the same place for a bit of time, but say you had some bad rust on a vehicle and parked it in the same place all the time, rain and snow dripping off of the rust could be rust-stained and stain the concrete.
There are rust stain removers for concrete, and for minor staining, I've heard of using lemon juice or vinegar and scrubbing with a brush
Thanks for the note. Yes, the situation involves the same vehicle with rust parked in the same spot. I have noticed new rust stains where the vehicle regularly parks this past summer so perhaps rain, as you say, dislodges some of the vehicle rust and deposits it onto the concrete driveway. I have never heard of this kind of situation before, so I'm not sure how common it is. Moreover, unless the rust is repaired at considerable expense, the rust transfer will just continue.
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There are rust stain removers for concrete, and for minor staining, I've heard of using lemon juice or vinegar and scrubbing with a brush