Aren't his songs owned by a label? Did he really keep all the rights, so he was able to do what the text above says?

If not, do we know which subset of his work is free?

EDIT:

His Wikipedia page lists the following labels:

- TransRadio

- Lehrer

- Reprise/Warner Bros.

- Rhino/Atlantic

- Shout! Factory

- Needlejuice Records

His sheet music was published by Crown Publishers Inc.

His public domain dedication is a noble gesture, but legally it probably doesn't mean much.