What type of "evidence" do you want?
In the UK you need to have a PSV to legally carry paying passengers all of the UBER drivers i had didn't had it (it's a sticker on the car window with the license number).
https://www.gov.uk/psv-operator-licences/overview
In the US passengers can be sued for damages when being involved in car accidents and cannot sue the driver unless they are paying passengers (which UBER doesn't qualify since it is not a licensed transport service)
http://personal-injury.lawyers.com/auto-accidents/when-you-a...
Whats worse is that since the passenger solicited the trip they can be made as the "cause" of the accident in civil suits when there was no gross misconduct on the side of the driver.
There is no easy way to obtain insurance information about UBER drivers, and unlike taxis in which the token ("car") owner is also liable in a law suit you cannot sue the car's owner if it is other than the driver with UBER in such cases when the car doesn't have proper insurance or wasn't maintained properly.
On the other hand you can get the insurance information for any taxi easily e.g. from NYC.
http://www.nyc.gov/html/tlc/html/industry/vehicle_insurance_...
The list can go on and on and on, UBER was playing it fast and loose with the law by pretty much ignoring it and shifting all of the responsibility on it's users and drivers.
The users don't know anything heck they don't even know that they might be breaking the law in certain places. The drivers well the drivers don't care UBER exploited places where getting a taxi license was expensive due to regulation as well as an economy in the toilet which presented them with a large user base needing additional income.
Public transportation is messy yes, but it's also heavily regulated and for a good reason because when it's not people can get hurt very quickly. GL getting a taxi license with a DUI under you belt or while being on the sexual offenders list, but you can still drive UBER....
The same way no one would use an UBER like service to get a doctor if they knew they could get a med-school dropout or some alcoholic that lost his practice due to malpractice suits however they are perfectly fine with getting into a car with a stranger at 2am knowing that unlike a registered car hire service or a taxi they weren't screened, it's not recorded in public records available to the local police and that they aren't covered by insurance and can be named in a law suit if anything happens during that trip.
Oh and this is without even getting into other things like UBER pissing over employment and taxation laws, doesn't verify that drivers do not work over the maximum amount of hours allowed by law, do mandated pit stops on long trips, maintain their cars etc...
My personal experience using UBER in London:
Driver hitting a cyclist and "contemplating" a hit and run.
Driver selling out weed out of his car.
Driver who was clearly working for at least 10-12 hours falling a sleep at the wheel.
Driver who was also working for just-eat or some other food delivery service carrying pizza and curry and asking me if i don't mind him stopping on the way.
Driver who had an open can of beer in the central console (didn't enter that ride).
I don't use UBER anymore i use the black cab / car service hire apps depending on the time of day and the location they aren't considerably more expensive (less than 10% on average unless you'll take a very long ride)
and they are all registered businesses with all the due diligence required.