/proc/mounts allows no distinction between regular mounts and bind mounts. That leads to having the same filesystem discovered multiple times. On some platforms this can potentially be worked around by parsing /etc/mtab, but that's not as reliable, as it does not represent the kernel's view.

Bind mounts were introduced in Linux 2.4.0 (man 2 mount). /proc/self/mountinfo was introduced in 2.6.26 to solve the problem of not being able to recognize bind mounts. Please also refer to this discussion: https://bugzilla.redhat.com/show_bug.cgi?id=491924, particularly comment #20.

The findmnt utility might bring some inspiration for how using different sources of information, including mountinfo, can be implemented.
http://man7.org/linux/man-pages//man8/findmnt.8.html