Client in question found a public domain icon they really want to use as their logo (instead of having one designed, I know, I know). Is this legal?
If it is truly in the public domain (or has a public domain notice) you can use it for whatever you want. So yes, it’s legal.
It may not be all that smart, though, given that anyone else can also use it as their logo. You may lose a good chunk of ‘uniqueness’ in that regard depending on the particular market you are in.
Using a public domain icon of a scale may be fine if you are a lawyer, as lawyers rarely compete based on branding.
But, on the other hand, if it’s a product logo to be sold on a shelf, being able to differentiate oneself visually may be very important.