Correct. Also, some states (such as mine) allow co-employee suits.
Depending on the assets of the co-employee, a suit could be possible.
Generally, WC is the exclusive remedy, regardless of the presence or absence
of negligence. There may be exceptions for gross negligence, or wanton and
wilful conduct on the part of the employer, depending upon the state.

IANAL, but from what I've heard, worker's
compensation insurance is often the "exclusive
remedy" allowed for workplace injuries.


Depending on jurisdiction, and I don't do any work for California clients,
you usually need to have a third party involved for negligence claims to
come in. Where that often hits the employer is that some sort of waiver of
subrogation is in place where the employer has indemnified the third
party.