First, you would deduce that the software in question has the ability to edit public user posts without the user's knowledge. You then read through the Terms and Conditions of said service to see if this capability is mentioned or not. If it is, then your lawyer immediately asserts that someone else, without your knowledge, changed your post, and the T&C says this is possible. Bad news for social media company.
Otherwise, you issue a subpoena for the source code for said software, asserting that you need to prove that this capability, in fact, does exist. Of course, the company will fight tooth and nail to prevent this. Even worse, they can change the code to remove any such functionality before answering the subpoena. So you really need to subpoena the version control history for the software going back to before the event in question occurred (probably reasonable to ask for changes up to 1 year before the incident).
However, if you can find an insider who will simply admit that this capability exists, then you have a star witness. The larger the company, the more likely that such a person exists, and has no particular loyalty to the company (and may themselves be disgruntled). Such a person would work in Operations. You can also subpoena documents related to Sarbanes-Oxley (SOX) controls. Every tech company needs to maintain legal info on who is able to access sensitive company data or not, because the CEO needs to certify that everything works as advertised. This allows you to find out how accessible the message database is, and who has write access to it. Everyone with direct write access becomes a potential suspect.
You don't need to wade through the entire source code to make your case. You just need to find the bits that can write to the message database, and see what controls exist. Almost certainly, Operations folks will have this capability themselves, to fix urgent problems during outages. But most likely executives will also be able to order underlings to make directed changes. Pretty much every system in the world works like this without exception.
Your lawyer will not be able to prove who did it, but that's ok. What they will do is demonstrate that a large number of people have the capability of writing to the database without leaving logs of their activity, and this means that any insider is capable of spoofing you. At this point, the corporation will not want this fact to be widely publicized, so they will likely offer to settle.