The rest of the album wasn't recorded and mixed during that time. They remixed those songs with Cornfield at Sawmills, but then went on to record the rest of the new songs with John Leckie at Real World Studios and The Astoria, a houseboat studio. This is taken directly from Out of This World, page 116 and 117 in the 2014 edition.
Also, on the musewiki page for OoS it literally says: "New Born", "Plug In Baby", "Bliss" and "Darkshines" were recorded with David Bottrill in the middle of touring in late 2000, in Ridge Farm Studios, Surrey. The songs were recorded as if in a live situation, within a few days. The band later had to re-master the songs with John Cornfield after the tour was over, in order to make them suitable for release, as they were not satisfied with the mixing of these tracks. Matt attributes this to the effects of the hallucinogenics, which were "great for exploring new territory", but "certainly not good for finishing things off".
It doesn't say that "Some songs like PiB and Bliss are re-arranged from the versions the band had being played live", it says that the songs were recorded as if being played live.