I've seen multiple reports from channel owners who have not been given any such option; the message saying that the supposed "rights owner" has confirmed the dispute is presented as "final" (along with the copyright strike). Unless this has changed recently, or there's some obscure link to switch to the DMCA process?
The only exception I'm aware of is a special agreement Google has with UMG where they ignore counternotices and appeals, but they also don't count as strikes and won't hurt the account in that case.
Describing it as "won't hurt the account" is a bit misleading. They won't nuke your account ("at this time"), but they also won't let you post the legal non-infringing content that the cartel has paid Google to suppress. That would generally qualify under the broader meaning of "harm" that applies during legal disputes.
It may hurt you in that sense, but not the account. I think it's pretty clear what I meant by that. Regardless such cases are fairly rare, vast majority of cases I've seen people complaining about YouTube issues have nothing to do with the UMG deal and I haven't heard of any other companies than UMG subject to this.
