"It is my understanding that the latest National Electrical Code recommends
connecting all grounds together.
Someone will be certain to correct me if I am wrong."
You are not wrong. You are correct. All grounds should be bonded (connected)
together at a common point.
All grounds include the electrical service entry ground, telephone equipment
ground, cable or satellite TV system ground, ham radio station ground, tower
ground, pool equipment ground, well pump ground, etc., etc. If the
individual grounds are connected to more than one ground rod, all ground
rods must be bonded (connected) to each other with a large solid conductor,
something like AWG 6 (or larger) solid copper.
Jim K9YC has an excellent article on this topic:
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