Copy/pasting a stroked path from Illustrator works OK only if the stroke is centred on the path.

If the stroke is set in Illustrator to align with inside or outside of path, inDesign pastes a closed shape. Means to get an accurate path you have to changed the stoke alignment in Illustrator, then copy/paste, then change the stroke alignment back in inDesign...

Illustrator CC2018 v22.1
inDesign CC2018 v13.1