In general terms, it isn’t really. Or at least it is a controversial topic still subject to discussion.
https://opensource.org/blog/public-domain-is-not-open-source
As to this specific topic, the fact that all of the code has to be open source is part of the 10 criteria https://en.wikipedia.org/wiki/The_Open_Source_Definition
As such, you can’t consider open source the public domain portions of a codebase that also has proprietary portions.













IMO once you look past the fact that they are both cursive and elegant, they are many differences. Taylor Swift’s signature has some very distinctive features, and none of them can be found in the brand’s logo, which is in a much more generic cursive style.
But I suppose the claim isn’t outlandish either, just seems very petty and either insecure or greedy.