Relativists do seem to be in trouble with having to live with a relative notion of truth for their own claims. But I am not sure that Allen's worries are decisive. Suppose the claim is that there are no absolute truths, but there are truths relative to standards that you and I accept. You can try insisting that you adhere to a valid standard according to which my claim is false. But then we could argue about whether that is right. Insisting is one thing, being rationally persuasive is another. Similarly, I might claim that a given proposition really will be true by some standards and really will be false by other standards and further say that that claim itself is true relative to standards that we both accept .. but false by others.
This sort of relativism might not be motivated by a desire dogmatically to insist that one has a right to one's own opinion ... it might be motivated by deep philosophical views about the relationship between language and/or thought and reality ... I think this would apply to most philosophical relativists, like Quine in some of his moods.