afaik, the VR unit comes with a break out box and one reviewer said this was because the original PS4 wasn't powerful enough.
That 'reviewer'(there are no actual reviews yet) was quite wrong.
The breakout box does have some processing capabilities, but it's nothing that adds to the graphics capabilities of the PS4. It 'dewarps' the image coming from the PS4 so that it displays a normal 2d image on your TV for others to watch. It also handles the 3d audio capabilities, which does save some CPU cycles, but nothing too dramatic.
The base PS4 is definitely powerful enough to run PSVR.
PSVR = Single 5.7 inch 1920 x 1080p OLED screen?
worrying
What's worrying, exactly? Keep in mind this OLED screen is 120hz and it also has an RGB subpixel structure, compared with the pentile structure in the Vive/Rift. What this means is that while the resolution is a hair lower on PSVR(1920x1080 vs 2160x1200), in actual use, it is entirely comparable in terms of clarity.
Of course rendering resolution plays a big part in how a title looks, and this is where the base PS4 will be disadvantaged some. Higher end PC's will be able to run higher resolutions, sharpening the image and reducing aliasing/shimmering. PS4 Pro will also have this capability. But that doesn't mean the base PS4 will look awful or anything. I've tried it and thought it looked entirely acceptable(in comparison to Rift/Vive).
That said, if you've never tried VR before, then you should be warned that perceived resolution is quite low in VR at the moment. Think more like a 480p image.
Also worth noting that the optics in the PSVR are very good and play a significant role in helping the image quality. Screen door effect(being able to see the pixels and the gaps between them) exists, but was no worse than on the Rift. This obviously isn't affected by what is powering the device, so there's definitely going to be a good quality experience even with the base PS4.
Last thing I'll say is that the base PS4 will be doing 60fps -> 120fps reprojection in a lot of games(particularly any graphically impressive ones). This works quite good, but is not perfect. It can cause certain artifacts in motion but from what I've seen and from impressions from others, it's entirely acceptable. PS4 Pro potentially has the capability to run these games at a native 90fps instead of 60fps reprojected, which *will* look and feel a bit better, but I would guess most titles use the extra power for pushing higher resolution rather than trying to push 60fps to 90fps(or 90fps to 120fps).
