Fitting rival car parts, half a century ago

When I was a teen, someone told me that a certain part (grille or bumper?) from a certain old ('40s or '50s?) Plymouth would bolt directly onto the corresponding place on a Ford, and vice versa. That is, this part (I want to say the grille – though it could be the bumper) would look as if it belonged on the car with no fitting or drilling.

I know that’s precious little information, but can anyone say if it’s true?

I could be wrong, but I think that custom car guys found that a Pontiac grille fit well into a '49 Mercury. In any case, it was pretty common to use the grille teeth from another car to make a custom grille.

That sounds very close to what I remember. Thanks.