Maybe he should be offended, but it isn't really him who's dead and that guy died being a hero for mankind so honestly, he can't find it in himself to get that worked up about it. Plus he's still distracted by the whole Hulk-ette thing. However, what she says seems more significant somehow. Mostly because Bruce is usually too paranoid to drive even after mostly taming the beast.

"Are you Hulk's girlfriend or something? Not that I'd begrudge him it, but I do remember Bruce swearing off romance after his ex's dad became a super villain. Unless that never happened... Car accident?" Maybe if he just keeps asking questions she'll forget he's not supposed to be here.