Places I have worked mostly require salaried employees to report hours no matter what, whether or not they're even eligible for overtime.
I have been salaried for nearly 20 years now, and have never, in that time, been required to report my hours.
The way it's worked for me is that I've been asked to report my hours when the information is being used to track how my time was divided among different projects. The ostensible purposes were to show that each project was receiving the its allocated share of resources. A secondary purpose was to see if anybody was being overworked -- for instance it could be used as evidence to justify hiring another person.
But we were told in no uncertain terms that we were not counting our hours. I'm sure the legal department had approved all of the verbiage and procedures.
I never personally measured my work in hours, and a lot of workers simply reported hours that precisely matched their project allocations, or copy-pasted from one week to the next. My present job doesn't have any of that.
Some companies who do that have both salaried and overtime eligible hourly employees who are otherwise in the same type of position. Or they did at different points in time.
So the meaning of saying that it is not counting hours is as clear as mud.
It also extends to more than one industry. Not just, say, corporate litigation.
It is perfectly possible to be a salaried employee, and to be eligible for overtime.
My interpretation: Companies just hate doing that, because it means trusting the employees to accurately report when they work overtime who are not regularly reporting their hours.