The guy should go for the hit streak imo. If it's your own record on the line, why give it up? I remember Carl Everett breaking up a no-hitter vs Mussina in the 9th with 1 or 2 outs at Fenway. That was awesome.
And the guy who laid a bunt down on Schilling when Curt had a no hit bid going...you don't just lay down and let the pitcher get it. I think most guys want to break it up whether they have a streak going or not.