Even (in)famous forgeries aren't worth much. Art is all about who touched it.

To be safe, I think the picture should be awarded to Peter Doig. Perhaps on the grounds that the owner admits it confusable with his brand..

He should team up with the family and make a collection called "Pete come Peter" - composed of Peter's reinterpretations of original works by Pete.

So if I make art "in the style of artist <x>", then all my work belongs to that artist?

(I'm not talking about blatant copies.)

Normally no, but here the "owner" was claiming it is the artist's work, not a facsimile or reproduction. So this is an exact case of the normally theoretical ill that trademark and brand related law is supposed to protect against: something that is honestly confused with the work of a manufacturer with a substantial cost to that manufacturer.

Try doing this at the border with a "rolix" and that offended manufacturer has rights to protect their interests not a responsibility to show up to convince customs that your rolix is a real rolex from back when they had trouble spelling. So I'd say this is an example of different justice for different relative social status.