relative clauses - Grammatically, why does it seem that 'that' can't follow the verb expressing propositional attitude in this sentence?

Consider the sentence,

Together with corroborant documentation, the petitioner must submit his own account of the events that he claims (that) justify the exemption.

That can follow any verb that expresses a propositional attitude. (E.g. 'He believes/expects/knows/says/claims/asserts/ that.')

However, I suspect that something grammatical -something other than stylistic concerns about repetition- prohibits the use of that after claims in the sentence above.

Does a grammatical rule prohibit the use of, or require eliding, that in the way I've described?

Thank you

-Hal