In the top photo, I've got my head up to focus on where I'm going. I used to ride this way all the time. In the bottom, I'm shrugging my shoulders and relaxing my head, looking up to look forward. I can see fine, it's just I'm looking up instead of straight. In the top photo it actually seems my arms are more bent (sloppy of me). Yet despite this advantage, you can clearly see my head is higher above my back: the difference to the bottom position is a full 5.6 cm.
With a head width of 17 cm (which I measured), Cd = 0.8, air density = 1.1 kg/m³, I can calculate the effect of a 5.6 cm drop in head position on power, assuming power depends on frontal cross-section and the head down allows more of my torso to draft. The result: 6.7 watts @ 45 kph.
Chasing to close gaps is always a dicey proposition. Small differences get amplified, since it's speed difference rather than speed which determines how long the chase will be. 6.7 watts can easily make the difference.
None of this is new, of course. Here's a photo of Jacques Anquetil setting the Hour Record: