Learn English – What meaning is “legitimate(ly)” gaining

I'm familiar with the following meanings of legitimately

In a way that conforms to the law or to rules

and

In a way that can be defended with logic or justification; fairly

(both from ODO)

But recently I have seen legitimately and legitimate used to mean something else. I can't tell if it's just an intensifier, like very (adv) or extreme (adj) or if it's being mistaken for another word, or what.

Below are some examples. Can someone pinpoint this emerging meaning?

TIL some children have such a legitimate fear of math that brain scans actually show their amygdalae (fear centers) activate when faced with a math problem.

(reddit)

This isn't using legitimate to mean a fear that conforms to rules, nor is justifiable, because neither of those things would affect how it shows up in a brain scan. The strength of the fear would affect that.

I look like I'm legitimately scared of food.

(BuzzFeed)

This isn't about legality or justifiability because that cannot be conveyed by a look.

I legitimately think whoever designed Yeezys did it for a bet. "I bet you can't design the worlds ugliest shoe and sell it for $2,000."

(Clint Evans, twitter)

This isn't about legality because we don't have thought police. It could be about justifiability, but semantically is seems more likely to mean honestly or really.

While the uses are different, they seem to be converging to a similar meaning. I just can't quite figure out what it is.