@Mrzilla,
If the bad numbers are more or less evenly distributed over the population in whatever are the significant demographics (age, gender, education level, what have you), then it kinda doesn't matter.
As for the client having the polling company write the survey and interpret the results, I'd say that's less likely to be biased, as the polling company is less likely to have a stake in any particular outcome. The polling company's stake is solely in getting the attempt at a poll accomplished. The number of people who answer the phone is probably not material to them, nor is it how the called persons answer the survey; all that matters to the polling company is just that they make the attempt.