Must the plan pay for distribution fees or can the participant be charged the fee?

I think the answer is no.

But I suggest you look on the 401k Message Board. Going back about the last 6 months, there are a few different discussion threads on the topic of administrative fees.

There was a request for an Advisory Opinion from the DOL on this topic, but I haven't heard anything for years. The DOL originally said that you couldn't charge participants for distributions, but I bet they backed off because that position makes no sense in a shrinking plan because it shifts the costs from the leaving participants to the remaining participants. I don't see a policy reason to punish long-term participants to benefit short-term participants.