Apparantly, allegedly, although personally I reckon it's partially urban myth, yes a thinner oil (as in lower viscosity) will, should, possibly, perhaps give better return on fuel usage in a newish engine on first start and prewarm up driving...
The numbers on the oil (5w40 etc) show its 'thickness' or viscosity when cold (the first number) and when warm (the second). So 0W is 'thinner' cold and so offers less 'drag' (and also flows to all parts of the engine better) at start-up. But if the second number is the same (eg 40), then either oil will have the same viscosity when warm and so make no difference to mpg of a warmed-up engine. (which is, I think, what greyrider2's pub conversation was all about). Note: If the 'warm' value is too low, the oil can 'break down' and stop lubricating effectively -- the dermining factor here is outdoor temperature. In warm climes like the UK, oils with a '30' rating may be too thin in cars that are driven hard.
The 'official mpg figures' are obtained by 'driving' a car (which has to have been 'run in') on an officially certified rolling road, following a prescribed set of speed curves, as defined in the EU standards, starting from cold - the total journey is just 11km (see here:
http://www.vcacarfueldata.org.uk/information/fuel-consumption-testing-scheme.asp). Although it must help, it is unlikely that oil alone can give the 5mpg difference, nor (more significantly) reduce the CO2 emissions from the engine. Fiat must have done more, and altering the ignition 'timing' or fuel mix in the ECU, maybe using different compression ratios, or changing the valve timing (different camshaft), or even different gearing, are, I suspect more likely the ways in which the improvements are achieved.
Previously, cars were tested for consumption at 56mph, and all manufacturers optimised cars for best economy at this speed. I'm sure car makers now know how to optimise mpg and CO2 when following the EU curves, but that most users will not see these figures in real life situations