In general, you do not need to get permission to include a copyright notice when redistributing a piece of BSD-licensed software. Indeed, if it were necessary, then you could not satisfy the license's first mandatory condition without permission, which would cause it to violate both Free Software and Open Source definitions. So, we can be certain that either 1) both the OSI and FSF have gravely misunderstood the BSD license text or 2) you can include copyright notices without running afoul of the no-promotion clause.
However, it may still be possible to display your copyright notice in such a way that it suggests promotion. For example, if your software used a library made by Google, it would be very misleading to include a message where you present the name of the organization in way that suggests endorsement, like
"Based on Foo Library, copyright GOOGLE, INC., 2011" (That's as big as Markdown will let me make it, but imagine the name perhaps ten or fifteen times larger.)
Whether a particular copyright notice display could be reasonably considered to imply endorsement is a decision made by a judge. If you are still worried that your unobtrusive copyright notice might be confused for endorsement, you might include a disclaimer alongside the notice like:
While this software is based upon software developed by
<organization>, this software distribution,
<your software name>, is in no way endorsed by
Any similarly-phrased is certainly a helpful step toward indicating a good-faith attempt to follow the conditions of the license. Whether it's enough to protect you against all judgments in all jurisdictions seems impossible to say (and certainly not possible for a non-lawyer like me to say).
If you're still worried that you might attract legal attention, then consult a lawyer, who can give vastly better advice that strangers on the Internet.