Of course discussion of Romney's business record is legit, given the centrality of his business experience to his argument for his candidacy. If he is going to say he should be President because he was successful in business, it is worthwhile to assess how he came to be successful.
The criticism from the Obama camp is not arguing that Romney's business tactics should be illegal or looked down upon. But it's to indicate that much of his expertise is in fact in destroying businesses, not building them as he claims in his stump speeches.
Romney rarely ever talks about his time as the governor of Massachusetts, and of course he never talks about his life in the Mormon church. The centerpiece of his candidacy is his time at Bain. So how could it possibly be that Obama's the bad guy for discussing every aspect of Romney's experience?