Some important details escaped my attention when I saw that intersection for the very first time.
Firstly, signs posted next to pedestrian "request crossing" buttons explicitly state that "scramble" mode is active for some period in the morning and in the afternoon. I presume that during these periods the intersection always uses "scramble" mode when it decides to allow pedestrian traffic.
Secondly, yes, there are dedicated diagonal pedestrian signals for diagonal crosswalks. I simply missed them previously. And yes, in "scramble" mode all pedestrian signals display "walk" signal (including the diagonal ones), while all vehicular signals become red.