Speaking to Lib Dems around Westminster, their main concern is that the Tories' outreach programme could start to look like a land-grab. The conference is their chance to speak and listen to the party leadership, they say, and they don't want any Tories wedging themselves into that process. But they do seem keener on having a Lib Dem minister, maybe Nick Clegg, speak at the Tory get-together in Birmingham. To them, that would show that the smaller party hasn't been subsumed by the larger one, and that it has an independent contribution to make to the process of government. It would symbolise that, as Danny Finkelstein put it, "there is a space for the Liberal Democrats as champions of liberalism".
In any case, you can expect more attention to be paid to this issue over the summer. The choreography of the party conferences is relatively petty stuff – but the message it sends out seems to matter deeply to scores of attendees, as well as to the government. As with all forays into uncharted territory, both sides will want to tread carefully.