Double electron-electron resonance (DEER) spectroscopy measures the distribution of distances between two electron spins in the nanometer range, often on doubly spin-labeled proteins, via the modulation of a refocused spin echo by the dipolar interaction between the spins. DEER is commonly conducted under conditions where the polarization of the spins is small. Here, we examine the DEER signal under conditions of high spin polarization, thermally obtainable at low temperatures and high magnetic fields, and show that the signal acquires a polarization-dependent out-of-phase component both for the intramolecular and intermolecular contributions. For the latter, this corresponds to a phase shift of the spin echo that is linear in the pump pulse position. We derive a compact analytical form of this phase shift and show experimental measurements using monoradical and biradical nitroxides at several fields and temperatures. The effect highlights a novel aspect of the fundamental spin physics underlying DEER spectroscopy.