Not related in any way to actual organizations of any actual tribes.

Most people know that there are more than one chef in the kitchen, yet we still figuratively say there are too many.

This is silly and trivial. Two reasons:

[1] The phrase is the analog of an idiom. It is shorthand for "hierarchy" and used as such. The parent is explaining its use.

[2] There are many tribal organizations. This cuts both ways. Provided there is a single one that was historically rank-hierachical, the data is not even a counterfactual.

[3] Provided [2] is ok, so is [1]. We know [2] is ok. Hence, the comment is logically ~gratuitous.

See, for example:

http://www.usingenglish.com/reference/idioms/too+many+chiefs...

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I don't think the correct response when called out the use of a racist stereotype is to claim it's silly and trivial.