Chat context can be easily forged

Imagine this:

<Steve> Do you want some diamonds?
<Alex> Yes.

The chat log above technically contains: UUID, message, timestamp, salt, and a signature of all these information. Signatures cannot be forged or it would be the end of cryptography. However, nothing prevents a player from forging the chat context by cherry-picking and signing another message with a modified timestamp:

<Steve> Do you want some diamonds?
<Baddie> You mean you are a white supremacist?
<Alex> Yes.

Now the player Baddie can report the message and get Alex banned.