I have to give this to the Punisher. While Green Arrow is incredibly skilled and has enough trick arrows and aim to put nearly anyone down, Frank has the experience over him. He's seen it all. He's taken on Hawkeye and probably a dozen other archers time and time again, and would likely be able to adapt to being shot at by crazy-ass arrows. Frank can take a ridiculous amount of damage and keep on going through sheer will/determination. He's also willing/determined to see his hunt through to the bitter, bloody end. Hel, he nearly took out the Avengers recently, just about on his own.
Additionally, OIiver seems the type to get a little cocky (much like a lot of the archers in comics) from time to time and would probably view this as an easy finish, somehow looking to trap the Punisher with a trick arrow right off the bat. If his first shot isn't a lethal blow, he's likely done for the minute he goes in to apprehend his prey, if Frank doesn't escape sooner.
You're too kind, Acid. Someday I hope to come back in and contribute again. I still add images here and there, but big-time Wiki edits don't fit on my time table these days. You do great work (as do the other contributors) and should be proud to be one of the Hulk's heralds. :)