In 1 Kings 2:13-25 when Adonijah asked Bathsheba to ask Solomon for Abishag as a wife, Solomon saw the request as tantamount to a treasonous attempt on the throne.

Given that Bathsheba was aware of Adonijah's previous attempt on the throne, why did she agree to relay the request? Why didn't she see it the same way that Solomon did? Or was the whole point that she was trying to tip off Solomon as to Adonijah's treason? If that was the case, though, why the pretense of relaying it as if it were actually a serious request?

Alternatively: why did Solomon see this as treason and Bathsheba didn't?