Hi I'd say you are exactly right. ' phrase will sound as if it refers to the next substantive noun, which is 'we'. So it rather looks as if we were lying by the side of the road when we saw the wheel - We saw a car wheel lying by the side of the road ...
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Mr. TomseemsMaybe they all thought that we were lying by the side of the road. Or they were distracted by the fact that Mr. Swan directed their attention to a completely different part oflikethat none of them objected to this: Lying by the side of the road we saw the wheel of a car.