If I am hit by your acquaintance while they are giving you that free lift, their private insurance will cover my medical bills for as long as needed.
If I am hit by a taxi from a regulated company, their business insurance will cover my medical needs for as long as needed. The fact that they have adequate insurance is something that is checked by the taxi licensing people.
If I am hit by an Uber driver, well who knows how much insurance they have - Uber covers them for $1Million but that doesn't necessarily cover even a year in medical expenses or long term care, so I am left recouping the cost of my care from the Uber driver themselves. Uber drivers are not regulated or inspected (yet - wait for that shitstorm to hit Slashdot when it happens) so there is no guarantee that when you get into that Uber car you are actually insured at all.