One problem with this is that it cedes the initiative to the company and allows them to anchor the negotiations with a number of their choosing. In the absence of any reliable information on what a reasonable salary would be at the firm in question, this might be the only approach possible. However, if you do have an idea of the range of salaries that might be possible, you can anchor the discussion at a higher initial value, leaving open the possibility of doing better than "base offer +5K" that is the best possible outcome with this approach.
I think one should also have a better opening line than "I don't know, you're in a much better position to judge my worth to the firm than I am." Something along the lines of "I can do x, y, and z for you and my skills are in demand in the current hiring climate. I think that I am worth $xx to your company."
"The range for this position in the market is x to x, is that the range for this position?" But, that could / may have been used or brought up in an earlier interview. Talk up your worth or unique skill-set before a verbal offer is made and establish you are "high range" as a candidate.
I think one should also have a better opening line than "I don't know, you're in a much better position to judge my worth to the firm than I am." Something along the lines of "I can do x, y, and z for you and my skills are in demand in the current hiring climate. I think that I am worth $xx to your company."