I wouldn't be surprised if some parents felt what could be interpreted as jealousy. For instance, my parents had a really rough time growing up; then moved to a foreign country where they could barely speak the dominant language, while pregnant, with no friend or familial or financial support... They carved out a place, worked their behinds off-- and as a result, my sister and I have had an incredibly luxurious and cushy upbringing (especially when compared to how my parents grew up).
In that regard, I do believe that some parents wished they had the same luxuries and opportunities that their children have.
But no, I don't believe that a truly caring parent could ever begrudge a child or be truly jealous of one.