The phrase "take BSD-license code and distribute it under GPL" is ambiguous. If one interprets it as "swapping the license from BSD to GPL with your name attached as its licenser, even if no code has been changed", it makes little sense, and it's likely invalid.
However, according to the legal experts at Software Freedom Law Center: If one makes a copyrightable change to the original software, or if one incorporates 2-clause or 3-clause BSD-licensed code (4-clause is GPL-incompatible due to the "advertising clause") into another copyrightable software - then yes. In these cases, the end result can be redistributed under GPL as a whole.
But it's worth noting that it's a result caused by the additional changes under GPL, and it's not a property of the original code under BSD. The copyright status of the end result would be a combination of "unmodified parts are still licensed under BSD by its original authors, and the modified parts are licensed under GPL by the new authors."
Since this is the opinion held by Eben Moglen and Mishi Choudhary, I'd consider it highly trustworthy (Eben Moglen was the lawyer-in-chief at FSF).
In the article Maintaining Permissive-Licensed Files in a GPL-Licensed Project: Guidelines for Developers, Software Freedom Law Center also gives explicit instructions for redistributing BSD-licensed code under GPL.
Including unmodified permissive-licensed files
First, SFLC states that, if the original work is not modified, its rights are reserved solely to its original copyright holders, and the original BSD-license must be preserved and followed exactly.
The simplest case of notice preservation is unmodified incorporation of a permissive-licensed file from an external project into a GPL’d project without making changes to the code in the file itself. Here the developer should simply leave the file with all notices intact. If the external project uses the single COPYRIGHT file method, the developer should copy the names of all the copyright holders from that file and place them, along with any copyright, permission, and warranty disclaimer notices required by the permissive license, at the top of the incorporated source file. This may require the developer to list a large number of copyright holders, but it is always best to err on the side of inclusion of each person who might have a copyright claim.
The top of the incorpoated file should look something like this:
/* Copyright (c) YEARS_LIST, Permissive Project Contributor1
** Copyright (c) YEARS_LIST, Permissive Project Contributor2
** Permission to use, copy, modify, and/or distribute this software for
** any purpose with or without fee is hereby granted, provided that the
** above copyright notice and this permission notice appear in all copies.
** THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL
** WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED
** WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR
** BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES
** OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
** WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
** ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
Adding GPL’d modifications to permissive-licensed files
If copyrightable modifications have been made to the original BSD-licensed code, these modifications can be licensed under GPL. In this sense, end result would be covered by GPL as a whole.
But the BSD-license in the unmodified part of the code is still under its original license, thus the original license must still be preserved and followed exactly. The modified end result under GPL is a superset of the original in the sense of both its code and its license.
A more complicated case occurs when a developer makes copyrightable
changes to a permissive-licensed file that the developer is
incorporating into a GPL’d program. Developers in this situation
typically apply the GPL to their modifications. (However, it is
possible for the developer instead to contribute new code under
permissive terms, such as the permissive license that governs the
unmodified file. We discuss that case in § 2.3.)
Even though the permissive license of the external project grants
legal permission to incorporate code from that project into a GPL’d
project, the developer of the GPL’d project must nonetheless comply
with the notice preservation requirement in the permissive license. In
a project that uses the file-by-file method, a developer who makes
copyrightable modifications to a permissive-licensed file should place
a new copyright notice and permission notice above the existing one
and should make clear that the developer has modified the file. The
top of the file will then appear as follows:
* Copyright (c) 2007 GPL Project Developer Who Made Changes
* This file is free software: you may copy, redistribute and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation, either version 2 of the License, or (at your
* option) any later version.
* This file is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with this program. If not, see .
* This file incorporates work covered by the following copyright and
* permission notice:
* Copyright (c) YEARS_LIST, Permissive Contributor1
* Copyright (c) YEARS_LIST, Permissive Contributor2
* Permission to use, copy, modify, and/or distribute this software
* for any purpose with or without fee is hereby granted, provided
* that the above copyright notice and this permission notice appear
* in all copies.
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL
* WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE
* AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR
* CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
* NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
It is very important that the developer preserve the entire copyright
notice, permission notice, and warranty disclaimer as they appeared in
the original code, as required by the permissive license. We sometimes
see GPL notices mixed in with permissive license notices—a confusing
practice that obscures both the provenance of the code and the precise
permissions that were granted by the various copyright holders listed
in the notices.