If it's true, the email being sent out to the wrong people is not your fault. Why should you suffer consequences of that. The team should bear the consequences of their actions.
Upon realising the email was sent out to "everyone" which was not their intention, why did they not send another another to correct the mistake and avoid further exposure. By letting it stay, they then have actually made the offer even if the offer was by mistake.
As it stands, an offer was made and you accepted. If you performed as per instructions on your end, they should suck it up and fulfill their end of the bargain.