Here is a question from the Baron's GMAT Pass key book
Q: Crossing the street, a car almost Struck us
A. Crossing the street, a car almost Struck us
B. A car almost struck us, crossing the street.
C. As we crossed the street, a car almost struck us.
D. A car, crossing the street, almost struck us.
E. Having crossed the street, a car almost struck us.
I actually think that D is also correct. Imagine the case of an accident happening because a car on the other side struck us, when we were putting on our shoe outside the temple or when we were gazing at the billboard standing on the pavement. One can say imagination is not allowed on GMAT because you have to avoid external data. But if the correct answer were to be arrived at(even going by the content of the book), imagination is what is driving its answer as well. In fact, the original answer is slightly more verbose and choosing that would actually have gone against one of GMAT's SC pillar rules: Brevity.
Now for the billion$$ qquestion: How do we handle questions such as this one on GMAT?
I picked C but I see your point.
However, it's not common in English to say "a car crossed the street" Generally people cross the street. A car can drive across a street.
I think D is wrong for a modifier reason though. I don't know the exact rule, but for non-essential modifiers we usually use ,which ... ,
So I would see it as " A car, which crossed the street, almost struck us"
A car that crossed the street, almost hit us.
Hope this helps.