I thought it should be read differently, then I read it more carefully and I agree with your reading. But since seeing the same thing said multiple ways often helps, let me present it my way. First merlyn's example, formatted differently.

lambda {
    context $socket;
    writable {
        print $socket "GET $url HTTP/1.0\r\n\r\n";
        my $buf = '';
        readable {
            my $n = sysread( $socket, $buf, 1024, length($buf));
            return "read error:$!" unless defined $n;
            return $buf unless $n;
            again;
        };
    };
};
[download]

Here it is again with comments stating what each piece does according to my understanding.

# This sets up one of many parallel closures that process
# in parallel.  It will be called at the start.
lambda {
    # This sets the context of what connection this happens
    # on.  This association is remembered within the engine.
    context $socket;

    # writeable sets up a possible event to monitor, when
    # $socket is writeable, execute the closure.
    writable {
        # The engine discovered we can write, so do so.
        print $socket "GET $url HTTP/1.0\r\n\r\n";

        # This variable needs to stay shared across
        # multiple invocations of our readable closure, so
        # it needs to be outside that closure.
        my $buf = '';

        # readable registers another event to monitor -
        # that $socket is readable.  Note that we do not
        # need to set the context again because when we get
        # here, the engine knows what context this command
        # took place in, and assumes the same context.
        readable {
            # This closure is executed when we can read.
            my $n = sysread( $socket, $buf, 1024, length($buf));

            # If we return without registering a follow-up
            # handler, this return will be processed as the
            # end of this sequence of events for whoever is
            # waiting on us.
            return "read error:$!" unless defined $n;
            return $buf unless $n;

            # We're not done so we need to do this again.
            # Note that the engine knows that it just
            # called this closure because $socket was
            # readable, so it can infer that it is supposed
            # to set up a callback that will call this
            # closure when $socket is next readable.
            again;
        };
    };
};
[download]

And here we see the reason for the nesting. You nest whenever one action is contingent on another having already happened. Given that lambda just registers a callback, and you always want to do something, somewhere, you always nest at least once. But you can nest more times.

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