ISIS' credibility would have suffered an blow if the claim had been immediately debunked. And I would think their credibility is already at an all time low right now because of their loss of Raqqa.
Credibility is important for ISIS both for recruiting and fund raising.
how soon after the shootings did ISIS take credit for it?
ISIS have apparently been promoting this type of attack on concerts in the US for a while. Some US Islamists have been rounded up while working on same though they were a group of more than one.
ISIS may be claiming credit to help m8tivate their minions to work harder to accomplish similar.