(Please note: I am not a lawyer, nor have I consulted one for this answer.)
Both should be true.
HearPlanet, by running it through their reading software, does get a copyright on the content they produce. Since the audio is a derivative of Wikipedia content licensed under the GNU Free Documentation License (GFDL), however, the audio must itself be licensed under the GFDL.
Since it's (automatically) licensed under the GFDL, you should be allowed to copy and redistribute it further—but you must credit *both Wikipedia authors and HearPlanet* for the recording.
That being said, some cross-referencing with HearPlanet's Terms of Use (< http://hearplanet.com/terms >) do cast this in a muddy light—for obvious reasons, they claim copyright on their work in general. In particular, the following sentence might be problematic: "Company Content may be derived from other sources but is protected by copyright as a collective work and/or compilation, pursuant to U.S. copyright laws, international conventions, and other intellectual property laws." I'm not sure how rules relating to compilations would apply, but it's probably not a problem for individual recordings.
This probably doesn't mean much given the repeated noted exceptions (e.g. "other than as allowed under intellectual property laws" or "Content provided by third parties may be covered under separate license(s)"). HearPlanet doesn't own copyright on Wikipedia content, and the GFDL is quite explicit that additional restrictions can't be added to the content. HearPlanet is certainly allowed, however, based on their Terms of Use, to discontinue service to you at any time for whatever reason.
EDIT: thekohser is quite correct that, under the GFDL, it is the authors who should be credited. I have to watch for minor omissions like that. :) I've therefore updated my answer to read "Wikipedia authors" where it previously read "Wikipedia". On a related note, sometime this year Wikipedia is expected to shift to the similar but simpler Creative Commons Attribution-ShareAlike license, in which case attribution by link may be acceptable. Read about the licensing update at < http://meta.wikimedia.org/wiki/Licensing_update >.