Crop factor gives an equivalent FOV/enlargement, not an equivalent perspective per-se as that is solely dependent on subject distance.
Crop factor cannot account for lens specific distortions... i.e. you cannot force a 50mm to distort like a fisheye lens does regardless of the distance it is used from.
I would have to see an example image to entirely answer the question. Perspective "distortion;" things like larger nose/smaller ears, are due to a short subject distance and a difference in the distance to other things w/in the scene. I.e. if you take an UWA picture of a perpendicular flat wall from 5 ft away, the distance to the wall is only 5 ft along the lens' centerline. If you instead measure a line from the lens to the edge of the FOV the distance is much greater.
Lens distortion tends to be the obvious bending of straight lines; barrel/outward bending or pincushion/inward bending... it does affect everything, but is most apparent in straight lines.
Perspective distortion will be the same regardless of the lens/crop as long as the cropping (in post, with FL, or crop sensor) is towards the center of the composition.