CH01::Lightweight clients: direct connection to P2P network not required

SPV verification doesn't require connecting to a full node over the P2P
network.  Many clients connect to specially designed tranasctions
servers (e.g. an Electrum server) which provides them with transactions,
SPV proofs, and headers--and provide relay for outgoing transactions.
Update text to remove claims about direct P2P connection.

ch01.asciidoc

@@ -242,18 +242,17 @@ hour--but offers complete autonomy to its users.
 Lightweight client:: ((("lightweight
 clients")))((("simplified-payment-verification (SPV)")))A lightweight
 client, also known as a simplified-payment-verification (SPV) client,
-connects to Bitcoin full nodes (mentioned previously) for access to the
-Bitcoin transaction information, but stores the user wallet locally and
-independently creates, validates, and transmits transactions.
-Lightweight clients interact directly with the Bitcoin network, without
-an intermediary.
+connects to a full node or other remote server for receiving and sending
+Bitcoin transaction information, but stores the user wallet locally,
+partially validates the transactions it receives, and independently
+creates outgoing transactions.
 
 Third-party API client:: ((("third-party API clients")))A third-party
 API client is one that interacts with Bitcoin through a third-party
 system of application programming interfaces (APIs), rather than by
 connecting to the Bitcoin network directly. The wallet may be stored by
-the user or by third-party servers, but all transactions go through a
-third party.
+the user or by third-party servers, but the client trusts the remote
+server to provide it with accurate information and protect its privacy.
 
 [TIP]
 ====