it depends also on wheather your ground clip is connected with the
chassis and thus the mains ground of the scope or not.
Expensive scopes and those battery operated are floating, so one can
connect the clip to what ever needed, but cheap scopes have only one
common ground and this might cause the problems.
If the unit under test is not connected to any ground reference common
to the scope, then ground clip is must otherwise you have no reference
for your measurement.
So if you have simple scope and it is connected to mains and its
chassis is grounded via mains ground, then you have to connect the
clip on the car ground in order to measure something.