This part of the white paper is broken. Satoshi was wrong. Accepting unverifiable "alerts" from network peers as a trigger for doing large amounts of computation is a significant DoS vulnerability.
For this sort of scheme to work you would have a small-to-transmit, easy-to-verify proof of the invalidity of a block. (Called a "fraud proof" among developers who have looked at this.) Bitcoin protocol as specified by Satoshi does not allow for the full range of fraud proofs necessary to support this sort of DoS-resistant lite node implementation.
https://www.merriam-webster.com/dictionary/peer
> one that is of equal standing with another : equal
If you aren't running a node, you're not equal, and therefore, by definition, not a peer.
What problem do you have with people running the blockchain they prefer?
>>As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.
While you claim that light clients betray the vision of Satoshi, based on totally unsubstantiated claims about what Satoshi meant by a light client, that are contradicted by several pieces of evidence (e.g. Satoshi communicating with Mike Hearn about Hearn's implementation of the SPV light client concept, without once claiming that his implementation fell short of Satoshi's idea of a light client, and while continuing to promote light clients on Bitcoin talk, like in this instance: http://satoshi.nakamotoinstitute.org/posts/bitcointalk/345/), you promote a future where the vast majority of the world have zero control over their own wealth, because they can't economically control their own private keys.