My mom was 37 and my father was 38 when I was born (in 1958). My dad aged hard -- among other things, he went bald in his 20s -- and was frequently mistaken for my grandpa. He got a kick out of it, and out of correcting people who made the assumption; I think he was proud of the fact that his "boys could swim" enough to father a child in middle age.
I am much younger than my siblings (born 1941, '44 and '47) and all but one of my nieces and nephews are within 2-10 years of my age, so it's understandable that I'd be mistaken for another grandchild when the real grandkids are my contemporaries.
I was kind of an oddball growing up, being so far removed in age from my sibs, but with the preponderance of divorces and second families in recent years, it's no longer so rare for someone to have a sib or half-sib who's almost old enough to be his/her parent.