On my last full-house stripping job, one of the sides had a painted cat-walk style deck floor. As I was pressure washing off the stripper from the siding, the first couple board of the cat walk, next to the siding, also lost all the top coat of paint. The stripper seems to have softened it to a point where pressure washing it easily took it all off. The rest of the paint that didn't get stripper on it wouldn't pressure wash off so the stripper must have worked on that paint. Perhaps it was solid stain, but I'm pretty sure it was latex whatever it was. Just one experience, so I'm not trying to dispute what PP is saying. I just thought it might be worth testing.
For applications of heavy quality paint, or multiple coats I wouldn't even try messing around with stripper. But if it's just one thin coat of failing behr, you might get lucky.