If yours does, I would still read the fine print and compare with ones on insuremytrip. I picked a random CC and read its benefits, and did not see one involving serious illness - only death, accidents, and things like flight delays.
Edit: Checked again: Apparently mine does provide travel insurance. But as expected, not for serious illness (e.g. stroke that requires medical evacuation - happened to someone I know during travel). Also, it only covers issues related to the mode of travel. So if you're in the Bahamas for 2 weeks, and you get into accident a week in, that is excluded. With insuremytrip plans, the whole duration of stay is covered.