Earlier quoted context omitted.
Why shouldn't a programmer be reliant on their tools? What a bizarre idea. I like to measure a carpenter's skill based on whether they can build a nice looking bookshelf with just a pocket knife said no one ever.
If you're asking them to design something rather than build something off a pre-existing design, you might like to know that they actually understand the principles of design, and aren't relying on a tool to pretend they do.
This could be an issue with really fancy IDE features, but there's a world of difference between a whiteboard and an IDE - namely, a text editor and an interpreter/compiler.