grammar - Is this correct? "One of the things that makes him great is..."

One of the things that makes him great is he brings it every night.

I'm pretty sure it should be that make him in the plural, because one of the things is referring to a lot of things and a lot of things should take a plural verb. But I always hear native speakers in America say it in the singular, so with an s.

Another example:

This is one of the responsibilities that comes with greatness and he understands that.

Native speakers always use the verb in the singular (here, comes) even though [I believe] it is grammatically incorrect to use the singular form of the verb there.