You would have to prove the agent mislead you by producing evidence the comps or other on market availabilities (for extrapolation purposes) where not fact.

They will almost always demand that you show evidence to justify the increase in value.

Ashley, if your inspector came back telling you to do that, It sounds like you have a huge foundation problem, swayback roof/floors, rafters pulling away from the ridge board, house with old wood floor beam and evidence of termite tubes, or even an ex owner that took out a load bearing wall.  

In the unlikely event that they sue me, how would this play out in court considering I have no evidence other than my word?

Do you have evidence they are living there, or can they claim that they are just guests?

Your personal credit card statement is the audit trail for your additional contribution to your capital account on you books of the business and is evidence of the expenditure for audit purposes.

@Adam Jaken I'm interested to know what empirical evidence you have to support this claim?  

You just have to use comps other than your own sale price as evidence of value.

We are in the inspection phase of a purchase (offer pending inspection) and found evidence of an undisclosed old fire in the attic that had been repaired.

The second time it happens, file a noise complaint with the police and try to record with video as evidence.