Perhaps a better question is "Do quad bikes present an unacceptable risk in a certain scenario?" All items from chainsaws to paper, carry some level of risk (those paper cuts hurt!) 'Dangerous' would imply a level of inevitability of an incident, versus risky meaning a skilled, trained and conscientious operator could use it for decades without incident.

Taking 'dangerous' in a simple context of the question, I would tend to agree that the level of danger depends on the use and comparison with similar farm equipment.
They're a lot less dangerous than the original Trikes, which had a habit of bouncing and rolling when cornering, but offer less protection than side-by-side farm vehicles in an accident. Much like other vehicles, they're designed to be used within certain operating conditions (speed, terrain, loading etc), for which they ought to be perfectly 'safe' to use. Use them outside of those parameters and the risk increases.
In agreeing with the statement, I'd repurpose a quote from 'The Castle' - but it's what you do with it!

Kia ora team,
Here are some links to stats associated with Quad bike injuries and fatalities.

From discussions with my learned friends it is because they do not come equipped with Roll Over Protection Systems (ROPS).

They can be fitted but it used to cause some problem with the warranty.

I find it ironic that all the photos on Worksafe and a few other sites have Quads with ROPS fitted.

The sad statistic is that a number of children every year die from quad bike related accidents.
Captured in the Australian data, not NZ Worksafe data

https://data.safeworkaustralia.gov.au/interactive-data/topic/quad-bikes
https://data.worksafe.govt.nz/editorial/quad_bikes

After having a look at the data you can draw your own conclusions.

Sadly, this argument is reminiscent of the NRA's false dilemma regarding firearms: 'guns don't kill people, people kill people,' used to justify their continued circulation. Humans are thrilled by speed, but often overlook that our bodies haven't evolved to withstand forces greater than running speed without a high risk of injury or harm. Historically, injuries and fatalities from riding horses, flying bi-planes, and driving motor vehicles have persisted without serious questioning of real versus perceived risk. Enclosed vehicles, like Todd Conklin's crash-proof Volvo example, are relatively safer today. Therefore, I think that quad bikes should be considered a failed transport experiment and relegated to a display at MOTAT.