off-chain payment channels: Do we need to trust "Payment Service Providers"? A paper entitled: "Privacy in Bitcoin Transactions: New Challenges from Blockchain Scalability Solutions" has tried to investigate privacy issues of the Bitcoin influenced by the solutions for scalability of transaction throughput such that off-chain payment channels.

In this paper, we read:


  "Mixing services as described so far can be applied to standard
  bitcoin addresses and transactions but when off-chain payment
  channels are used, such mixing techniques cannot be applied in the
  same form. In off-chain payments, on one hand, users may be more
  restricted on the number of payment channels that they create (due to
  fee costs) but on the other hand, payments are processed with multiple
  hops through different Payment Service Providers, and such
  hops could remain secret since they take place in the off-chain payment network and there is no need to store them. So
  the natural idea to detach the link between source and
  destination in this scenario is to perform payments through secret
  multiple hop routes."


Of course, there is no need to store the intermediary hopes between source and destination. However, 

(1) What happens if those Payment Service Providers decide to reveal the information of the payment ? (if they are able to do ?)

(2) How to perform payments through secret multiple hop routes ? Does it mean that we need to trust the intermediary hopes to keep them secret ?
In lightning network payments are onion routed.  The only thing a PSV could reveal is the previous and next hop, but they can not know the origin or the destination.  They know it came from Alice, and went to Bob, but they do not know where Alice may have gotten it from, or where Bob may send it to.