I don't know what LT's official reason for this is, but I know why I would recommend resistance over cardio.
When you exercise on a VLCD, it appears to work in a different way compared to a low calorie diet, or at maintenance levels.
On a VLCD, your metabolism drops a fair bit (as expected), and it seems that there is a possibility that cardio exercise can cause a further drop. It also appears that it doesn't help fat loss either.
There seems to be a threshold between calorie 'in' levels that defies the normal cals in vs cals burnt theory.
As far as I know, 'they' aren't sure why this happens, but they think the body compensates for the lack of calories by dropping the metabolic rate throughout the day.
This doesn't happen with resistance, which seems to help metobilic rate from slowing too much. It will go down as per a VLCD, but not quite so much IYKWIM.
So, from what I gather cardio can do more harm than good.
Of course, if you have a trainer who is an expert in VLCDs, he/she may well have good advice about what sort of cardio/how long etc would work