So...we have here a car with a factory 289 where it "should" have a 260 for a build date prior to August 1964 and 4 lugs....I am not sure I would immediately jump to the conclusion that someone swapped 6 cylinder components on. My personal guess is that it was a base 6 cylinder car the customer ordered with an upgrade to the 289
From Wikipedia

take it with a grain of salt)
In 1964, an intermediate performance version of the engine was introduced with a four-barrel carburetor and 9.0:1 compression, rated at 210 hp (157 kW) at 4,400 rpm and 300 lb⋅ft (407 N⋅m) at 2,800 rpm.
The engine was an option on the 1964 1/2
Ford Mustang and was known as the "D-code" from the letter code used to identify the engine in the
VIN.
[2][3]
The D-code engine is relatively rare, as it was only offered as an optional engine in the latter half of the 1964 model year.