my takeaways from that are as follows;
a) good tyres are better than bad ones (WITIKA)
b) If you are going to ride on gravel-strewn or otherwise very bumpy surfaces, wider tyres are better than narrow ones (WITIKA)
c) That they couldn't (or wouldn't) see a 1% difference in aero drag in the wind tunnel as statistically significant, between two tyre sizes that are not that much different from one another.
d) That they don't either understand or have looked at everything that makes a difference here. You can't just change one thing, then measure one aspect of performance and draw a conclusion about everything else, because those things won't all stay the same.
e) The summary has failed to mention several potentially important results (from both their own research and that of others), presumably because they don't really agree with the main conclusion they would like to see. Amongst those results are (IIRC); i) the lowest Crr tyres they have ever tested were a set of 23mm racing tyres, ii) that tests on some batches of GB tyres have demonstrated the exact reverse i.e.
that wider tyres are slower.
a) and b) WITIKA..? = 'Which I Think I Knew Already'.
In c) this says more about the inadequacies of the wind tunnel methodologies used and the chosen experiment as anything else. I guarantee that had they done a more sensible experiment to test the hypothesis that 'wide tyres are not slower' then they would have got a strong result. As it is they chose tyres that were only a little bit wider, in which case the true conclusion might be 'that tyres that are only a little bit wider might only be a little bit draggier' ..... WITIKA.... Had they wanted to find out the drag of 42mm tyres then they should have tested that, not the drag of narrower ones. However, if the photograph is anything to go by it isn't clear that the wheels were even turning in the wind tunnel tests, which IMV completely invalidates any conclusions you might draw about wheel drag; the top of a turning wheel is going at double the speed of the bike and can create a lot more drag, for example.
In d) I mean that they have not assessed the effect of wheel weight as a variable (and in fairness I can see why, it is complicated) but they also have not really allowed for the fact that when you fit a wider tyre to the same rim the wheel becomes a larger diameter, which also automatically lowers the Crr. IIRC both these factors (which flatter a wider, heavier tyre in coast-down tests) are not allowed for and are instead dismissed as 'statistically insignificant'. Well in isolation, each might be, but if you get enough of these things adding up, you can wind up drawing some duff conclusions.
For leisure riding, touring and bridepaths, I ride wide-ish tyres and I'm probably doing about 15-18mph a lot of the time. I don't like running wide tyres on skinny rims because the tyre can fold over during agressive cornering, and -contrary to what you might read elsewhere- it seems pretty evident that the external width of the rim (as well as the internal width) is important here. If I use a rim that is in constant proportion to the tyre width then the net weight increase is certainly signficant. Overall, on rough surfaces wider tyres are obviously better (I didn't need to be told this and nor should anyone else be...

) . I don't think wide tyres (32s rather than 25s say) slow me down very much the rest of the time either and if I'm more comfortable this is A Good Thing.
However as soon as you are planning to go faster than this, on roads that are reasonable tarmac, aero losses start to become more of a big deal. The wheels alone can account for tens of percent of the total aero drag and making them wider just increases that pro-rata (to a first approximation). The presently available tyres with the lowest measured Crr values on such surfaces are relatively skinny ones of about 23mm width. They are lightweight and have low aero drag too, when fitted on typical racing wheels. So if you are going racing that is probably what you should use, unless the roads are especially rough (i.e. 'normal' in some areas....

) in which case there may be a net benefit to using a slightly wider tyre. If the surface is particularly smooth then narrower tyres/rims may be of benefit (e.g. track racing). They may not have seen a 1% difference in drag in the wind tunnel as statistically significant but if you go 1% slower in a time-trial you might have dropped ten or twenty places in a close field. You
will notice that.....
Note that if you are planning to go slower than 15mph (perhaps sat bolt upright) then any rolling resistance benefit, even for part of your ride, may be a net gain because you may never go fast enough to incur any real aero penalty from wider tyres. Even if you do it will be a proportionally smaller amount of the whole anyway.
So overall, the answer to the question 'are wide tyres faster' is probably 'sometimes'. When the surface is rough and/or you are not
really in a hurry.
If you want to exploit this possible advantage then you probably need to spend a bit (or a lot) more on your tyres than normal, and you may well sacrifice some strength, damage resistance, puncture resistance, and overall tyre longevity in the process. This won't necessarily make the tyres 'inadequate' for the task in hand so I'm normally happy to pay a bit more for nice rolling tyres, even if they don't last quite as long; but if I was commuting on glass strewn streets in the hours of darkness I'd have different priorities.
If you ask a different question which might be 'are wider (say +5mm) tyres very much slower?' -in a touring context- then the answer is 'no, not necessarily'. So if they confer another benefit such as comfort or the ability to go down bridepaths, they are a good choice.
cheers