OTR allows is users to have strong authentication of encrypted messages
without the *additional risk* that normal digital signatures introduce.
Alice is no better off in the court scenario that you describe, using OTR
vs. not using anything, but this way she can use an encryption system that
doesn't expose her to greater potential danger, should the other party
defect.
Adam Back and I suggested a way of doing this with OpenPGP at Usenix in
1998: http://www.cs.ucl.ac.uk/staff/i.brown/nts.htm