The OP asks:
Can I take code which is licensed under a permissive open source license (like the BSD license) and distribute it under a copyleft free software license (like the GPL)?
Specifically, quoting the following from Wikipedia:
In addition, the permissive nature of the BSD license has allowed many other operating systems, both free and proprietary, to incorporate BSD code. For example, Microsoft Windows has used BSD-derived code in its implementation of TCP/IP and bundles recompiled versions of BSD's command-line networking tools since Windows 2000. Also Darwin, the system on which Apple's Mac OS X is built, is a derivative of 4.4BSD-Lite2 and FreeBSD. Various commercial Unix operating systems, such as Solaris, also contain varying amounts of BSD code.
And OpenBSD Journal:
KernelTrap has an interesting article in which Theo de Raadt discusses the legal implications of the recent relicensing of OpenBSD's BSD licensed Atheros driver under the GPL. De Raadt says, "it has been like pulling teeth since (most) Linux wireless guys and the SFLC do not wish to admit fault. I think that the Linux wireless guys should really think hard about this problem, how they look, and the legal risks they place upon the future of their source code bodies." He stressed that the theory that BSD code can simply be relicensed to the GPL without making significant changes to the code is false, adding, "'in their zeal to get the code under their own license, some of these Linux wireless developers have broken copyright law repeatedly. But to even get to the point where they broke copyright law, they had to bypass a whole series of ethical considerations too."
Specifically at stake is the question of whether or not is it legal to take a file or files licensed under a BSD licence, affix a GPL header at the top of such files without making any other changes to the content, place the GPL licence in the root and mention it in README, and distribute the results.
If such licence amendment to include GPL (in addition to the BSD licence) is not legal, then why Microsoft's and Apple's practice is.