These are the off-chain scaling issues, so relevant to both Bitcoin and Ethereum (and other blockchains).
That particular discussion is predicated on a very pure version of payment channel networks. One early assumption is around funding of payment channels, where a deposit is made only when the payment channel opens. In fact it is possible to add funds to an open payment channel, although this does come with an associated transaction cost.
Payment channel implementations will no doubt be slightly less pure than some would hope for, offset by the fact that they will work for a wider range of use cases.