Yeah, I'm currently facing exactly that dilemma. I have to model a database of machine parts.

There is a natural PK in the form of the supplier's parts number, but the legacy system (which uses that as PK) notes that it is specifically the parts number as used in the supplier's ERP system, but suppliers often use differently formatted parts numers in publications such as catalogs (adding or removing spaces, slashes or dashes). So the legacy system also has the "published part number" as one or more separate fields.

This inconsistency makes me lean very strongly towards using a synthetic PK instead.