As my friend once said, the only people bigger braggers than sailors are archers.
Not warbows, but self stick bows nontheless, have been used at our flight shoots for the past five years or so, with dozens of bow/arrow combos tested out, distances accurately measured. From the data I submit shooting 250 yards takes a good bow, very good arrows and a competent shooter. I've yet to see anyone break even the 200 meter barrier on their first try, no matter how strong and skilled a man. That being said, 250 yards is attainable by anyone who puts some effort into flight shooting.
I'd bet Piper's friend didn't shoot 250 with nail-headed bamboo arrows and twine strings any time he wanted to. I'd be willing to believe 125 yards (that's about the maximum range I reached with twine strings and nail-headed arrows at age 12). Eyes and steps are misleading, tape measures don't lie.
Tuukka