If it's a paraphrase, I'm not so sure it's a fair one.
In the United States, for example, we are urging people not to be tested unless they have severe symptoms. The reason for that is not to save money, but it's for a lack of testing capacity. As a policy we would much prefer to be testing even the mild suspected cases. But we don't (currently) have the testing capacity to do so.
So I think the lack of testing of mild cases (at least in the United States, and I suspect in other countries) is more a reflection of our rationing priorities than it is a reflection of our spending priorities.
If the testing capacity becomes unconstrained and we (or other countries) still fail to test mild cases.