What does it mean for the DFT phase to be relative to a cosine wave?
A cosine wave is an even function around the origin (X axis = 0).  The basis vectors of the real components of a DFT are all cosine waves that start at 1 at the first sample.  Imaginary components of DFT basis vectors are all sine waves that are odd functions around the origin 0, and start at zero at the first sample in a DFT window.

However, for strictly real input, you can add a phase offset p to a cosine wave function to make cosine(x+p) look like any ratio mix of real and imaginary basis vectors (cosine waves and sine waves) in the DFT result, and that phase offset is what this book is calling the DFT phase.

For even length FFTs of non-fictional data, I prefer to do an fftshift to move the phase reference to the middle of the FFT window, instead of leaving the phase reference at the potential circular discontinuity at the first sample of the DFT window.