They're correct.
External drive of some form is pretty much a requirement if you're planning on undeleting the majority of a drive, every write that happens on the main drive puts you further from recovering a file.
Even a stack of USB sticks would do the job if you have something else to use as temp storage for when they're full. So long as it's not an obscene amount of data you may be able to get away with only needing a couple.
As a note - if you're using the drive already you've lost a stack of potentially rescued files, and that's not taking into consideration background tasks OS' do (eg Windows automatically defrags drives in the background, and that's not good for undeleting)
You should probably think about using a cloud service for backing up important stuff in future.