The force from wind resistance should be more on the larger person. It should be proportional, at a given wind speed, to the ratio of their cross sectional areas.

The acceleration from a given force is inversely proportional to the mass of the body it is applied to.

The larger person has more mass and a larger cross sectional area. The question then is this:

Is Mf/Ms > Af/As,

where Mf and Ms are the masses of the fat and skinny persons, and Af and As are the cross sectional areas of the fat and skinny persons?

If Mf/Ms > Af/As then the fat person will feel less force from wind resistance at a given speed than will the skinny person.

Let's say my mass was 50% higher than my friend's mass. Unless my cross sectional area is also 50% higher than theirs, I'll experience less acceleration from wind resistance than they do at a given velocity.

If my increased mass came from just being bigger in all dimensions, I'd be 14% bigger in all dimensions, and have 31% more cross sectional area.

In reality, the increase in cross sectional area is even less than that. When you get fat you don't get taller. You get wider, but not as much as you get longer. Height and width are the ones that matter for cross sectional area assuming you aren't ridding side saddle.

Imagine a spherical cyclist ;-) Mass scales like the cube of its radius. Surface area (air resistance) scales like the square of the radius. As the radius (mass) increases, the air resistance becomes relatively less important.

Ignoring wind resistance is the problem. Undoubtedly mass was accounted for, but they got the incorrect answer because wind resistance has a much greater effect on the lighter rider. The extra momentum of the heavier rider easily overcomes the small increase in wind resistance. Anyone who has biked with someone of significantly different body mass will have seen ample evidence that bigger people coast downhill faster.