I found this from the FBO extension specs:
"Additionally, when rendering to or reading from an application created-framebuffer object,
-[…]
- There is no multisample buffer so the value of the implementation-dependent state variables SAMPLES and SAMPLE_BUFFERS are both 0"
So there’s no way we can do multisampling when rendering to a texture? This seems like a big limitation to me. Anybody found a way around this?