If the manual is saying small amounts of DOT3 can be used, what they are most likely saying is if you find yourself with low brake fluid and only DOT3 is available, it is better to use that than to not have brake fluid.
Once you get back home though you need to get the recommended DOT4 back in the system by bleeding the system and filling with DOT4.
As already stated, DOT4 handles higher heat. If your car is calling for DOT4, that means that the manufacturer does not feel comfortable that the braking system will not raise the brake fluid above a temperature that DOT3 can handle.
Another point to make here is there are two boiling temperatures for brake fluid, Dry and Wet.
When you've just replaced your brake fluid and the system has been properly bled, you are working at the Dry boiling temperature. Over time, water works its way into the system through age, heat cycling, through the hoses, etc. You are then working at your Wet boiling point for the fluid.
So again, if you get stuck in a spot where you need to put some new brake fluid into the system and all you have available is DOT3, most likely at that point your DOT4 has degraded some and the fresh DOT3 will be close to where the DOT4 is at, but this won't stay true, the DOT3 will degrade once in the lines so the above statement of replace it as soon as possible holds true.