Typically, we have been able to convince the owner to pay for it.  But you need to do a good job narrowing down the areas that truly require scanning so they don't think it's money wasted.  

We have occasionally convinced the contractor to pick up the tab for scanning because it really benefits the contractors significantly.  

Architects aren't usually responsible for surveying as-built conditions, therefore it seldom make sense for architects to eat the cost of scanning.  

Also, keep in mind that you can't do much with point clouds.  Try to get a scanning company to also convert their elements into use-able format models (Revit, 3D dwg, etc.), and preferably with information (it's better to know if the 2" pipe is hot / cold water, or gas, etc.)

Is the scanning company liable for construction liability if their stuff is not accurate?

Thanks for the reply Cat!

The scanning company is responsible for the accuracy of their scanning and modeling (if they've agreed to convert the point cloud to model for you).  So if the model they handed over says an elements is somewhere, but when construction commence it's actually 2 feet away, they should pay for the resultant additional coordination and potential change orders.  In their contract, there should be definition for allowable tolerance, which needs to be vetted with the contractor and could have pricing implications if the tolerance is super fine.