As written, I believe your own interpretation is the only correct one.
"what seems to be the fact that ..." indicates that the writer is suspecting but not yet sure that the observers' comments (i.e. what they observed) in fact means this particular fact he proposes.
However, if there was a comma before "that" as shown below, I think your brother's interpretation would be correct.
- Many observers have commented on what seems to be the fact, that fear plays a much smaller part than we should think it must in the life of an animal which lives dangerously.
In this case the "that" clause modifies the "what" clause, saying in effect "which is (the fact) that the fear ...".
Without the comma, the sentence stops at connecting the observations with a specific fact, whereas with the comma, it makes a contention that the interpretation the writer presents is a factual truth.
Both versions are viable sentences, but I think the version as written (without the comma) sounds more plausible.