Is it true that homotopy pullbacks and homotopy pushouts coincide in the category of spectra? I had a feeling that this is the case, but don't know where to find a proof or how to prove it. Thanks!
Although the answer is sketched in the comments, I wanted to remark that this statement is proved carefully by Cary Malkiewich as Proposition 6.2.11 in Parameterized Spectra, A Low Tech Approach. He credits Model Categories of Diagram Spectra as the first place this was proven, but I couldn't find the result there.