Avvo provides only one follow link, and that is in the person's profile. Links in answers are nofollow. As a result, answering questions on Avvo should not harm a site.
I answer a lot of questions on Avvo and it hasn't hurt my firm's site. I often put relevant links in the link section of my answers. For example, if I am answering a question about medical malpractice, I might put a link to a page I wrote on the basic requirements for a medical malpractice case. However, I do not put links to my firm in every answer. I only use links when I think the person might be a potential client for my firm and I would like to guide him/her to my firm's site.
I agree with irvingw that your client may well be doing this sort of thing all over the web, which might be the source of the problem. In addition, if your client is adding a general non-useful link back to his website, he might be violating Avvo's terms of service.
I see a lot of disavowing in your future.