In theory, the sheild to connector shell, carries stray currents, EMI/RFI/etc., that would be induced into signal conductors (by "waves-of-force" "cutting" through the wire). It happens more often at Radio Frequencies. Putting sheild to chassis ground, shunts this to earth ground (as long as a ground lift is not used). If a ground lift is used, then "safety ground" is floating, and can be anything from 0A to very high currents. (CURRENT KILLS not voltage)
What you commonly see is guitar amps with "lifts", and when the guitarist touches a microphone that is properly grounded, his BODY completes the circuit, and the "floating" ground that is carrying an actual voltage (for whatever reasons) is what gets carried (from the amp, thru the guitar, thru the GUITARIST, the mike can, to chassis ground in the console). Most gear has a "ground bus" that all grounds are tied to. Gear with multiple ground points, usually suffer corrosion or a loose nut, and that's what causes the buzz - a ground lift will lift EVERYTHING, so everything is floating (and in turn seeking a GROUND to complete the circuit).
I had a number of clubs I've worked in, bring in electricians to go through the entire system. PA gear on one circuit, lighting gear on another, backline on another - with a ground bond that ALL circuits get strapped to (I usually have them drive a ground stake (8 foot copper rod) into the dirt outside, and wire it to a 10 guage strap). All the buzzes go away. In most small clubs, it's the dimmer packs from the lighting system, that cause buzzes.
We did a 3 week safety course in Navy Electronics school, covering proper grounding. On ships it's real important, as the entire ship is grounded. If a piece of gear is "floating" anything else you touch can be hazardous to your health. I've gotten enough "electro-shock therapy" from bad grounding to avoid it whenever possible.
Sorry for the rant, it's really not a safety issue in portable recording, but properly constructed cables can make all the difference in quality recordings...
Rick