Is this a recent update for the PS3? In the past PS3's backwards compatibility always introduced three frames of lag, for both PS1 and PS2 games and regardless of the PS3's output resolution. So even in 480i on an SD CRT.
According to fubarduck, I think. Edit: and shidoshi, come to think of it.
I'm not sure, they might have improved it a bit. PSone Classics R-Types seems to be the same as it ever was, and I was playing my PS3 on a CRT back when I bought the game, but now I'm using a 17ms LCD, which despite being damn fast as LCDs go, obviously isn't as fast as a CRT.
It's not the resolution setting that alters response times though, it's the upscaling feature found in Settings > Game Settings > PS/PS2 upscaling.
I tested the upscaling option yesterday with the PS2 Classics CvS2, and it does make a difference when switched off. It's a small difference, only a couple of frames, but I could feel that the button presses were more responsive and the game more playable as a result. The downside being that you'll have to adjust the aspect ratio on your TV yourself, since the PS3 simply outputs at a SD resolution by default when upscaling is disabled.
Even stuff on the PS4 like Gradius and Ajax from the Arcade Archives collection aren't shown at their best on modern TVs. There's still that tiny bit of lag even on a good LCD or Plasma. It's something you really notice when you play these old-school precision arcade-style titles. Wii U's VC suffers the same.
It's a shame we're still hamstrung by LCD and Plasma input lag, nearly a decade after they started to go mainstream. Hopefully SED or FED or a more reliable, cheaper form of OLED will become practical to manufacture at some point in the future.