I suppose "lie on the floor" was a bit of an exaggeration. It likely would have involved the transfer of the seats, or at least the seat liners, from Starliner.

NASA didn't release much info on the contingency plans, but there was brief mention of it in an ARS Technica article a while back: https://arstechnica.com/space/2024/08/yes-nasa-really-could-bring-starliners-astronauts-back-on-crew-dragon/

NASA issued a $266,678 task award to SpaceX on July 14 for a "special study for emergency response." NASA said this study was not directly related to Starliner's problems, but two sources told Ars it really was. Although the study entailed work on flying more than four crew members home on Crew Dragon—a scenario related to Frank Rubio and the Soyuz MS-22 leaks—it also allowed SpaceX to study flying Dragon home with six passengers, a regular crew complement in addition to Wilmore and Williams.

In my opinion, the biggest risk unmitigatable risk would have been the lack of ports in Dragon for Butch and Suni to plug their Starliner IVA suits into.