For example, if someone was running a full node and somehow re-wrote the software so that blocks and transactions which did not abide by Bitcoin's consensus rules would be able to be relayed, what would stop these blocks from joining the Blockchain?
Is it the fact that these blocks are broadcasted to other nodes that stops the invalid block from joining. For instance, if the invalid block is relayed to a non-corrupt full node and this full node rejects it, then it won't be added <-- is this true?