In the Buhlman-Straub credibility model I get a relatively small (in relation to the within group variance estimate) and negative between group variance estimate.

The reason for the estimate being negative (since it is by definition positive) is the correction term for unbiasedness.

In what way would my inference of the credibility factors be affected if using an alternative but biased estimate (the within variance estimate is still small but positive)?

For some groups I do have a lot of data and should hence be quite certain that the residuals for these groups are credible estimates of the underlying risk profile.