glReadPixels() sets GL_INVALID_OPERATION error

I'm trying to implement color picking with FBO. I have multisampled FBO (fbo[0]) which I use to render the scene and I have non multisampled FBO (fbo[1]) which I use for color picking.

The problem is: when I try to read pixel data from fbo[1] everything goes well until glReadPixels call which sets GL_INVALID_OPERATION flag. I've checked the manual and can't find the reason why.

The code to create FBO:

glBindRenderbuffer(GL_RENDERBUFFER, rbo[0]);
glRenderbufferStorageMultisample(GL_RENDERBUFFER, numSamples, GL_RGBA8, resolution[0], resolution[1]);
glBindRenderbuffer(GL_RENDERBUFFER, rbo[1]);
glRenderbufferStorageMultisample(GL_RENDERBUFFER, numSamples, GL_DEPTH24_STENCIL8, resolution[0], resolution[1]);
glBindRenderbuffer(GL_RENDERBUFFER, rbo[2]);
glRenderbufferStorage(GL_RENDERBUFFER, GL_R32UI, resolution[0], resolution[1]);
glBindRenderbuffer(GL_RENDERBUFFER, rbo[3]);
glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH24_STENCIL8, resolution[0], resolution[1]);

glBindFramebuffer(GL_DRAW_FRAMEBUFFER, fbo[1]);   
glFramebufferRenderbuffer(GL_DRAW_FRAMEBUFFER, GL_DEPTH_STENCIL_ATTACHMENT, GL_RENDERBUFFER, rbo[3]);
glFramebufferRenderbuffer(GL_DRAW_FRAMEBUFFER, GL_COLOR_ATTACHMENT0, GL_RENDERBUFFER, rbo[2]);
OGLChecker::checkFBO(GL_DRAW_FRAMEBUFFER);
glBindFramebuffer(GL_DRAW_FRAMEBUFFER, fbo[0]);
glFramebufferRenderbuffer(GL_DRAW_FRAMEBUFFER, GL_DEPTH_STENCIL_ATTACHMENT, GL_RENDERBUFFER, rbo[1]);
glFramebufferRenderbuffer(GL_DRAW_FRAMEBUFFER, GL_COLOR_ATTACHMENT0, GL_RENDERBUFFER, rbo[0]);
OGLChecker::checkFBO(GL_DRAW_FRAMEBUFFER);

My checker stays silent so the FBOs are complete. Next the picking code

glBindFramebuffer(GL_DRAW_FRAMEBUFFER, fbo[1]);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
// bla, bla, bla
// do the rendering
unsigned int result;
glBindFramebuffer(GL_DRAW_FRAMEBUFFER, 0);
glBindFramebuffer(GL_READ_FRAMEBUFFER, fbo[1]);
int sb;
glReadBuffer(GL_COLOR_ATTACHMENT0);
glBindBuffer