Magnetic images of high density vertically recorded media using metal-coated carbon nanotube tips exhibit a doubling of the spatial frequency under some conditions (Deng et al 2004 Appl. Phys. Lett. 85 6263). Here we demonstrate that this spatial frequency doubling is due to the switching of the moment direction of the nanotube tip. This results in a signal which is proportional to the absolute value of the signal normally observed in MFM. Our modeling indicates that a significant fraction of the tip volume is involved in the observed switching, and that it should be possible to image high bit densities with nanotube magnetic force sensors.