When the term "grounding the antenna to the frame" is used it more properly means "grounding the antenna
bracket to the frame." The outer shield of the coax will be connected to the antenna bracket via the antenna mount and connectors and thereby to the body/frame. The wire inside the coax connects to the antenna and is not grounded.
All mobile and base transmitting antennas need a counter-poise, more commonly called a ground plane. The antenna is the reactive unit, the ground plane is the reflective unit. Both are essential and equally important. In mobile installations with standard antenna systems, the vehicle metal (body, frame, etc.) acts as the ground plane. In "no-ground-plane" systems, the coax shield is used for counterpoise.
Too many antenna mounts on jeeps are placed in locations that are easy but don't make a good RF ground connection. These include powdercoated spare tire carriers, swingaways, etc. The solution is good metal-to-metal contact and judicious placement of braided copper ground straps, a process known as "bonding." [Decent bonding will resolve almost all ground plane issues; there is absolutely no need to consider "no ground plane" systems in jeeps.]
Conceptually, think of a platform diver pushing off a platform. If that platform gives when the diver pushes off with his legs he won't get much lift or distance which results in a crappy score. If the platform is sturdy he will get height and distance when he pushes away from the platform and therefore more points. Its the same with radio transmission.
Here is a photo of my CB mount. It uses ring terminals rather than the typical SO239/PL259 coax connectors, but illustrates what those coax connectors do - the center wire to the antenna and the coax shield to ground through the antenna bracket.
Here is an article about bonding:
http://www.k0bg.com/bonding.html