"Brother" probably isn't the right word, more like "cousin." We all know that AA EXPs don't get the same benefits on BA as BA Golds, just like BA Golds don't get the same benefits as AA EXPs on AA (e.g., BA golds don't get free upgrades). I don't know why one would assume that a particular OneWorld elite level received certain benefits (i.e., waived checked baggage fees) without it explicitly being offered somewhere.

Lufthansa specifically outlines additional free baggage allowances for Star Gold elites. BA only indicates that BA Silver/Gold Exec Club members have additional baggage allowances, no exemption for OneWorld elites. I think many airlines don't extend additional baggage allowances to partner elites. Another example of someone thinking all frequent flier programs operate the same.