After more than a week of official silence, Apple responded Friday to widespread complaints about reception problems on its newest iPhone. Its answer, issued in a “Dear iPhone 4 users” letter, is surprising in several respects.

For one thing, it contains Apple’s (AAPL) first official acknowledgment that what Steve Jobs called a “non issue” is in fact a real problem:

“Some users have reported that iPhone 4 can drop 4 or 5 bars when tightly held in a way which covers the black strip in the lower left corner of the metal band,” it writes. “This is a far bigger drop than normal, and as a result some have accused the iPhone 4 of having a faulty antenna design.”

The cause of what this “dramatic drop in bars,” the company has discovered, “is both simple and surprising.”

Upon investigation, we were stunned to find that the formula we use to calculate how many bars of signal strength to display is totally wrong. Our formula, in many instances, mistakenly displays 2 more bars than it should for a given signal strength. For example, we sometimes display 4 bars when we should be displaying as few as 2 bars. Users observing a drop of several bars when they grip their iPhone in a certain way are most likely in an area with very weak signal strength, but they don’t know it because we are erroneously displaying 4 or 5 bars. Their big drop in bars is because their high bars were never real in the first place.

To fix this, we are adopting AT&T’s recently recommended formula for calculating how many bars to display for a given signal strength. The real signal strength remains the same, but the iPhone’s bars will report it far more accurately, providing users a much better indication of the reception they will get in a given area. We are also making bars 1, 2 and 3 a bit taller so they will be easier to see.

In short: it’s not the iPhone that is at fault, it’s the bars. And the owners who don’t know how to hold their phones.

Apple is offering a free software upgrade in a few weeks that will take away a few superfluous bars, but won’t change anything else. The signal attenuation problem will still be there. Users who have dropped calls or lost data connections by gripping the antenna will still drop calls and lose connections unless they buy Apple’s $29 Bumper or its functional equivalent.

Apparently, there will be no free Bumpers, which in any event are out of stock. In the meantime, a rubber bracelet with holes cut in it works pretty well.

The letter reminds iPhone 4 owners that if they are not fully satisfied they can return undamaged units within 30 days for a full refund. The letter does not mention any restocking fees [see correction below]. Nor does it guarantee that AT&T (T) will let them buy a new phone at the fully subsidized price.

I suppose that means the class action suits will proceed.

CORRECTION: Apple did charge a restocking fee for iPhones the first year. They do not charge it anymore. Sorry for my confusion.

See also:

• Linda and Kevin win race to sue Apple
• Lawyers seek iPhone Death Grip victims
• How bad is the iPhone 4’s signal loss?
• The iPhone 4 Death Grip saga

[Follow Philip Elmer-DeWitt on Twitter @philiped]