Full Idea
The claim 'that Fido is brown' seems to demand only a brown Fido, but Truthmaker demands more. It demands both that a state of affairs along the lines of 'Fido's being brown' exists, and also that this state has its constituents essentially.
Gist of Idea
Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients
Source
Trenton Merricks (Truth and Ontology [2007], 4.I)
Book Reference
Merricks,Trenton: 'Truth and Ontology' [OUP 2007], p.69
A Reaction
One would need to reread Merricks to get this clear, but my instinct is that the two scenarios are not very different. 'A brown Fido' would require Fido to be necessarily brown to do the job.