Well, Brandon's reaction was kind-of predictable, he was a person who acted without giving a thought for consequences. Rhaegar running off with/kidnapping Lyanna was the action that started the whole mess, he ran off with the daugther of a powerful lord who was coincidentally bethrothed to another powerful lord. Even if she went willingly, it was a slight for Houses Stark and Baratheon and it could not have been thrown under the rug, they had to do something about it. Yes, it was stupid of Brandon to ride into the Red Keep and yell for Rhaegar to come out and die, but it was even more stupid of Rhaegar to give him the incentive to do so. Robert's Rebellion started when Aerys demanded Ned's and Robert's heads from Jon Arryn, but that would not have happened if Rhaegar thought things through in the first place. The kidnapping (or not kidnapping ) of Lyanna Stark planted the seeds for the war that followed.