I had a look at the report and some of the sources they use. There's many problems which I won't bore you with. Standout one - they use modal share for travel to work three times in three separate indicators but it is just three ways of looking at the same thing. So, for instance, let's say Edinburgh has high % using car for work then it must have low % using PT and probably low % walking and low % cycling. The %s all need to add to 100%. Logically. So you can't use the same thing three times to score a place.
Public transport costs are used in a similar way - three ways of looking at the same policy of subsidisation - each used as a separate indicator.
The other perhaps subtler issue is how they construct the index. I'd argue that it is wrong to rank, add the rankings and re-rank. This widens gaps where cities might be quite close. They should have scored, standardised the scores, added the standardised scores and then ranked. If they were going to rank at all.
The link to the detailed methods paper was broken but it looks like a piece of 'research' constructed to justify an existing position.