Taylor expansions: unstable or not?

As I was gathering results for my Austin talk, I noticed that the observed "unstable" behavior of our Taylor expansions may only affect the order-bump-needing versions of the QBX FMM. Said differently, my theory is that if you do anything fishy, then the Taylor expansions will take worse revenge on you than other, more well-behaved expansions. But maybe, if you don't do anything fishy, Taylor is not inherently bad.

@mattwala, what do you think? Do you have any observations that would contradict this?