In sales, there is an old expression that says if you can’t prove it, don’t say it. This usually refers to the dialogue between a sales person and a prospect, but it is also applicable for a resume. As a hiring manager, you are well within your rights to ask candidates for documentation of the accomplishments they list on their resume. If they don’t have documentation, perhaps a request for a reference for that accomplishment is appropriate.
Checking every single accomplishment is over the top, but checking one or two accomplishments makes sense. I suggest those that seem the most impressive to you about the candidate be verified. If someone told me that they personally doubled the size of the company in one year, I would want to see proof of that!