Here's what I've got so far, bear with me using rmwhite's picture as the demo (thanks for the pic):
What seems to be the evidence so far that this could potentially (that's my disclaimer word, you know) is the issue and the fix is that it seems like many people, when looking at their microSIM cards and the trays they're mounted in, have noted that in some instances the actual contacts of the microSIM itself
could be coming into contact with the microSIM tray itself, which is made of metal as well, and causing a short. Here's a picture of what I mean:
The circled area, which appears as the vertical grayish-line, is the 'gap' between the side of the microSIM tray and the microSIM contacts - if there's nothing in there and the contacts are touching the microSIM tray or even so close that some electrical bridging is happening, that could be the reason why the problems are happening, and also why when some people "grip" the phone tighter they are literally closing that gap or causing it to decrease in width.
This could be the answer, folks...
ps
Just for the record: the microSIM in my iPhone 4 actually has a decent gap in there, and I placed a tiny sliver of notebook paper (and I do mean tiny) that wrapped around the bottom edge of the microSIM, completely covering the entire side, and barely edged over the top so the contacts were not affected when it's inserted, and still I have issues so...