It really depends on what is being amortized, a good portion of SHW intangibles come from the acquisition of Valspar, when you add back the amortization related to the acquisition you're including the benefit of the acquisition but turning a blind eye to the cost that allowed you to get that extra revenue, earnings, etc.
This is a little different of an example than what you asked but it kind of proves the point:
Imagine a rollup, they acquire other shops to grow, instead of all those cash outlays hitting the actual capex account it hits the acquisitions account in the investments section of the cash flow statement. Now all of the amortizations related to the acquisitions get added back the operating cash flow. Now imagine your trying to calculate the company's historical FCF over the last 5-10 years, and you just subtract capex from operating cash flow ignoring the cash outlays for all acquisitions but still including amortization of those assets related to those acquisitions that allowed you to generate that operating cash flow
Hope this helps somewhat.
