Unless, like with her seduction, the moment we stand up to her and refuse she drops the act and moves on to the analysis phase (though, as with that, we don't know whether it'd still be an act if we don't refuse)
I feel like if Jiraiya wanted to he'd have pretty good odds of forcing Ami to hold to this (does the letter have any uniquely identifying characteristics, or is it just regular script in Ami handwriting that could be faked?), and that there's also a pretty good chance if we say no then it all blows over. Quite possibly this is Ami telling Jiraiya that he's got a perfect opportunity to marry Hazou to her if he wants to, since Ami knows Hazou would take something like this directly to Jiraiya.
As a side note, we shouldn't go dramatic with Keiko and swear on our father's grave. Instead, we should initiate CCnJ and explain to her that a) we met with Ami to try and get information on her diplomatic faction for Jiraiya, b) we did not propose to her or do anything that could be considered a proposal during the meeting, and c) we're going straight to Jiraiya to get this sorted out.
Keiko may feel very frazzled right now, but she'll still understand that when we go CCnJ it means we have something to say and we're worried about subtext getting in the way of making a clear point.