The statement "in order to read, you need to verify the chain" most likely refers to light nodes - or clients. From the docs:
The purpose of the light client protocol is to allow users in
low-capacity environments (embedded smart property environments,
smartphones, browser extensions, some desktops, etc) to maintain a
high-security assurance about the current state of some particular
part of the Ethereum state or verify the execution of a transaction.
There are many differences between light and full nodes, but, primarily, it's about what data is synchronised. A light node syncs much less information than a full node, but that information is enough to verify that the data received from a full node isn't tampered with.
It's worth looking into block headers and merkle trees, especially the latter, because that's what's being used here.