Exactly! In fact, that's embarrassingly concise given my rambling. The only major thing missed is that the hash input has to contain something that the attack doesn't know in addition to the message. Or in other words, the private key is usually also involved in the hashing. If you ever want to get into details, the MAC [1] and HMAC [2] wiki pages go into depth.

[1] https://en.wikipedia.org/wiki/Message_authentication_code [2] https://en.wikipedia.org/wiki/Hash-based_message_authenticat...