I've heard Eric give the explanation that agrees with the DT quote. The first posting above might appear to provide a better "story" but given that Eric was an adult when he left Scotland, it just doesn't jive with anything Eric has ever said about the song's origins.

All this aside, it is a great song. Whenever I sing it, I always give the background but also tell the audience that while Eric's talking about his Mom, it has real meaning for anyone who's ever had to leave--or been left by---someone they love.