Your logic is solid, but their usage kinda implies the opposite (that skylights would make summers worse, not winters). That seems possible given the obvious dynamics of increasing the amount of direct sunlight, but based on a quick Kagi the overall effect is actually good for both summer and winter if used instead of windows rather than in addition to windows:

  Introducing skylights allows the total fenestration area (windows plus skylights) to be reduced from a maximum 20% of floor area to as low as 12% of floor area while achieving the same baseline average daylight factor target of 5%, and reduces annual heating and cooling energy use and costs in all but two of the 108 models with skylights analyzed. In other words, when different combinations of skylights and windows are used to achieve the same target daylight factor, the heating and cooling energy cost savings are almost always greater when equivalent daylight comes from top‐lighting (skylights) rather than side‐lighting (windows).