I thought it might have been...

In this video clip of the movie 'Coco', this conversation takes place at 41 seconds:

https://youtu.be/JX1JYdZvs9w?t=41s

[Miguel sees the Land of the Dead for the first time]

Miguel: This isn't a dream, then! You're all really out there!

Victoria: You thought we weren't?

Miguel: Oh, I don't know. I thought it might have been one of those made-up things, that adults tell kids, like vitamins.

Victoria: Miguel, vitamins are a real thing.

Miguel: Well, now I'm thinking maybe they could be.

Context: Miguel, a 12-year-old kid who is alive, is visiting the Land of the Dead and he's talking about how the dead really exist contrary to his belief that they are made up by adults.

In the underlined portion, I'd like to know the reason for using the verb construction 'might have been' in the subordinate clause.

I, for one, think 'might be' is the more natural construction, and here's why:

In direct speech, what Miguel is essentially saying in context is:

[DIRECT SPEECH] I thought, 'It may/might be one of those made-up things.' (I think either 'may' or 'might' is okay.)

Now, if this is expressed in indirect speech, simply using 'might' instead of 'may/might' would be natural, I think:

[INDIRECT SPEECH] I thought it might be one of those made-up things.

And I don't think that the past tense 'thought' doesn't warrant 'might have been' in indirect speech:

[INDIRECT SPEECH] ?I thought it might be one of those made-up things.

Which, however, is what Miguel actually says in the video clip.

Could someone please explain why?