What’s the definition of “cultured butter”?
We're not all going to agree on a definition of cultured butter, so these answers are going to be subjective.

Culture distillate (https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?fr=184.1848) and lactic acid are both used for flavoring.  Is cultured butter butter that tastes a certain way, or butter that's been prepared a certain way?

How about a more common food: would you call it smoked salmon if it hadn't really been smoked, but only flavored with liquid smoke?  There are reasonable arguments on both sides.  Perhaps you consider smoked salmon to be a dish made with salmon that tastes smokey, regardless of how it's prepared.  Perhaps you consider smoked salmon to be salmon that has been smoked, and you aren't really concerned with how it tastes.

Personally, I like to know what I'm eating (not just the flavor of what I'm eating).  Calling something cultured butter suggests something about how it was made (fermented with live bacteria cultures), so calling cultured-flavored-butter "cultured" seems a bit dishonest for my taste.