Employers are typically liable for misconduct by their employees occurring within the "scope of employment." For argument's sake, even if Uber drivers are considered "employees," this USC student may have a difficult time prevailing against the company at trial.
A sexual assault committed by an employee will only be attributed to its employer if the "motivating emotions" behind the act itself were "fairly attributable" to work-related events or conditions. The vast majority of sexual assaults in the private workplace probably don't meet this standard. However, a skilled plaintiff's lawyer might be able to find other reasons to keep Uber in the case long enough to force a settlement. Unfortunately, most commercial insurance policies do not cover assault and battery, so employers facing such lawsuits could get stuck paying out of pocket for their own defense.
The sad truth is that many employers are sued even though they don't appear to have done anything wrong. As long as a plaintiff's lawyer can keep the case alive long enough to force a jury trial, economic considerations frequently lead to some form of settlement. This is why employers have to be careful about which law firm they hire. A highly skilled but reasonably priced attorney could help an employer "fight the good fight" much longer than a more expensive lawyer. Just because a law firm has 100 or more attorneys doesn't mean it's a good fit for a particular client or case.