Sure, Macports is separate, excepting that if you can't download the Command Line Tools, Macports isn't going to be able to build you anything.
Anyway, in my case, as I have previously had an older Xcode developent environment installed into the old normal place, /Developer, my "xcode-select" was left on my system pointing to that old place, /Developer.
Now, because I wanted to 100% wipe away the old development environment, when I used the recommended procedure to do this ("sudo /Developer/Library/uninstall-devtools --mode=all"), it not only took away the /Developer directory, but also various developer tools such as /usr/bin/cc -- and so Macports, and of course *any* development outside of Xcode could not compile anything.
Anyway, then I tried to use the Xcode 4.3.2 presribed way to reinstall the "Command Line Tools", which failed, but I suspect it failed because my "xcode-select" was still left pointing to that old place, /Developer. I suspect if I had updated that to point to the new "Xcode developer home", /Applications/Xcode, that it would have worked.
But as it happens, I found the link mentioned previously to download the "Command Line Tools" manually.
After installing the package, I could again compile stuff, as I once again had a /usr/bin/cc, and the Macports worked again (as you might expect).
Interestingly, Macports pumped out a lot of warning messages at me:
Warning: xcodebuild exists but failed to executeWarning:Xcode does not appear to be installed; most ports will likely fail to build.
Warning: You may need to run `sudo xcode-select -switch /Applications/Xcode.app`
...and *that* is where I first heard about the requirement to be concerned with where "xcode-select" is pointing.
So, it may well be that Apple fixed something in the last several hours that has enabled the Xcode application's Preferences Download tab to download the "Command Line Tools" to work, but I suspect it is more likely that for those where it worked for them, they knowingly, or unknowingly, had their "xcode-select" set to the correct target directory.