This sounds like saying "There is no cloud, just someone else's computer". Or more on point for you, there isn't "a Mempool". Put more precisely there isn't a singular Lightning Network but many peer to peer networks. It is a network though or set of networks. Better yet, a type of network.
Is this a distinction that is helpful? I'm not sure saying it isn't a network is helpful in understanding it. I think we are on the same page but maybe explaining it differently.
I'm not an expert on Lightning so if I'm missing something I welcome feedback on this commentary.