Capricorn is ONLY their Sun sign, and how well/poorly that influence works depends mostly on how that person's Sun interacts with ("aspects") a of the other 9 planets.
However, ANY planet in Capricorn represents a part of the personality (each planet is a different need/facet) that TENDS to feel guilty.
Sun is our self-esteem, so Sun in Capricorn (born late Dec to late Jan, any year, any time, any location) tends to have inner doubt about their worth. And they often hide it from others, which can be overcompensating by trying to convince others and themselves too that they are proud. I very well-aspected cases, a Capricorn planet indicates shyness rather than guilt or self-doubt.
And any planet in Capricorn, the more it makes square and/or opposition "aspects" with other planets, the more guilt and self-doubt they have to combat and overcome.
Understand that all our chart indicates is how we are LIKELY to be IF we do not grow or change. Someone with Sun in Capricorn who APPEARS prideful in the ways you describe, most likely has not been adequately nurtured while growing up, perhaps resulting in a continual fear of inadequacy and guilt about him/herself, and quite possibly also has square and oppositions from other planets TO his Sun, indicating difficult finding an internal sense of self-approval.
In order to use Capricorn in understanding this person, you really would have to do up their personal unique birthchart and compare all of the 40-50 factors to your own observation of this person. Sun sign astrology is just a commercial scam and not real astrology.