Sorry about leaving it for so long but I was so busy implementing the goddamn algorithm, I forgot about this :)
So after reading up on Veach's thesis pretty closely, I understood what was going on. First of all Veach's thesis describes about BDPT using MIS. However I implemented without MIS using the techniques described in the original Lafortune's paper.
For a fixed strategy, you can end up consuming a different number of samples depending on your mutation. This can happen for at least two reasons. If your perturbation changes some material along the path to, say, a multi-lobe BSDF, you would need more samples to account for the lobe choice. This would shift everything by the number of extra samples used. If ...
The summation doesn't include the BxDF that was picked for sampling. Look again at this line:
if (bxdfs[i] != bxdf && bxdfs[i]->MatchesFlags(type))
Here bxdf is the one that was sampled earlier, so when it iterates to that one it skips it.