Macro on a Crop Camera - Is this correct?

[Alexander]

I understand that when using a macro lens that achieves a 1:1 image size on the sensor, the image is supposed to be life size. Is this still correct when using a 1.6x crop camera? I'm assuming that it is, but that the sensor is simply smaller. Thus, when enlarged to picture size, this is giving a larger image (?) of the subject (more magnification) than when used on a full-frame camera. Is this correct, or am I horribly confused?