This is exactly the right answer. If you can catch it you have already done all the work and expended the energy to match it's course. You need nothing else. The asteroid would provide zero benefit. This is pretty easy to explain even in calculous.

If you could generate enough delta-V to match the velocity then the asteroid would be useless. You have already done all the work. It would even be a hindrance because it would almost certainly not be going exactly where you want to go. Thus costing an immense amount of propellant and fuel.