I have tried multiple times now, and cannot replicate this issue on my iPhone 4.
I have held it in the left hand just as the video described and demonstrated, I have tried holding it in my right, I have tried bridging the left seam as well as the top seam (even simultaneously) with my fingers, and nothing. I have also tried it with WiFi, 3G, and EDGE, and no drop in any of them. I held it in the aforementioned ways during a phone call as well as during cellular data transmission. I never did have the phone lose any bars, have the call break up, or have my data transmission slow down. In fact, during a speedtest over 3G, I pulled 4Mx1.5M without breaking a sweat! (THANK YOU, Apple, for finally giving us HSUPA in one of your phones!)
Now, granted, I happen to be lucky enough to live in an area with good AT&T coverage in town...I get 5 bars in my house where I was conducting these tests. I did read about other people who started with 5 bars, though, and who lost a significant number of bars when they tried this. I didn't. Just in case it is an issue that can only be observed in conditions with marginal signal, I will try this again while at work tomorrow, where I rarely get more than 3 bars.
(My display on my iPhone 4 is gorgeous, too, with none of the blemishes that have been talked about. Not that I doubt they exist...I have had my share of iPhone hardware problems in the past, having gone through 6 total phones between 3G and 3GS models, with problems covering screen dust, malfunctioning switches and buttons, defective dock connectors, crappy LCDs, and failing sensors. I figure it's about time I got one that works properly.

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-- Nathan