Absolutely! Some travel policies won't cover certain types of losses that you might think they would, unless they offer additional coverage (for extra $) or you add a "rider".
For example, accidents during certain sports - scuba diving or jetskiing for example - are usually not covered on a typical travel policy (unless you add coverage). Renting a scooter on vacation in Siem Riep seems like a fun and practical way to get around. But, you might/probably need to add special coverage for it, as some basic travel policies EXCLUDE accidents on scooters. Another thing is coverage when riding a rented scooter or a vehicle that you have no licensing to pilot in the first place. I'm in SE Asia moment, where scooters are a dominant form of transportation. Scooter rentals are everywhere. But, technically, you need some form of licensing to ride these in most places, even if many locals don't have it. It's why the police are setting up checkpoints, and pulling over youthful riders (and sometimes impounding vehicles). Now, if you get involved in an accident on a scooter, and you need medical coverage or worse, medial evacuation, you better make sure your have coverage. Real coverage - not assumed coverage.
I worked in homeowners insurance in the last part of my working life, and was a licensed adjuster for a while.I have good grasp of what does and doesn't do. Insurance companies don't stay in business by paying out settlements where there is no coverage or when the policy holder is not covered for a specific loss. If your travel insurance provided by your credit card isn't clear on coverage (and it is an area of the insurance industry that hits me as rather opaque), then I suggest you opt for travel policy that does offer clear coverage. The cost is probably insignificant compared to what the whole vacation will cost you. I must admit, that I was slow to get wise to this, and traveled for many years without any kind of insurance. However, in recent years, I've had to seek emergency medical services overseas on at least three occasions and the monetary settlement always was more than cost of the policy.