You need permission to copy unless fair use applies
Does this mean that when someone sends you their resume, it is unlawful to pass it on to others unless the author gives permission?
First note that copyright law only applies to copying. If someone were to give you a physical copy of their resume (assuming such a thing would happen in this day and age) then giving this to someone else without copying it is not copyright violation. There may be privacy issues involved but that’s another issue.
Further, in the United States, there is a fair use doctrine which allows limited copying without permission in certain circumstances. This is likely to apply in a lot of situations around copying resumes.
Finally, permission does not have to be explicit. For example, if you receive a resume in the course of a job application then permission to make copies for that purpose can be assumed to have been implicitly given.
Can you get sued if the resume finds its way to someone the author did not intend to see it, and the author suffers some harm as a result?
Under privacy law, possibly. Under copyright law, no.
What you can be sued for is making a copy. It doesn’t matter where this ends up.
Is distributing a resume in the context of professional networking considered as implicit consent to allow sharing with anyone under the US legal system?
No. It’s explicit consent because those networking sites have Terms and Conditions that explicitly deal with copyright. For example, if you post your resume on LinkedIn, you agree to this.