What is the density profile within the Sun's photosphere? Which one of these is wrong?
I usually don't answer my own questions, but sometimes when the question itself is called into question I make an exception.
The density of the photosphere at $\tau_{5000}=1$ is predicted to be $3 \times 10^{-7} \text{g/cm}^3$ in the Holweger-Müller Model Atmosphere7.
As pointed out in comments there is a spread in values here.
The 1E-06 g/cm^3 density value (plot) is more consistent with  = 1 or &quot;bottom&quot; of the photosphere, while the density in the quote is more consistent with the cooler &quot;top&quot; of the photosphere (circa 4300 K).
From Chapter 2: The Photosphere of Timo Nieminen's thesis Solar Line Asymmetries: Modelling the Effect of Granulation on the Solar Spectrum



Figure 2-3: The Holweger-Müller Model Atmosphere
7 Holweger, H. and Müller, E. A. “The Photospheric Barium Spectrum: Solar Abundance and Collision Broadening of Ba II Lines by Hydrogen”, Solar Physics 39, pg 19-30 (1974). Extra points have been cubic spline interpolated by J. E. Ross. The optical properties (such as the optical depth and the opacity) of a model atmosphere are, obviously, very important, and will be considered later. See table C-4 for complete details of the Holweger-Müller model atmosphere including all depth points used.
8The height scale is not arbitrary. The base of the photosphere (height = 0 km) is chosen to be at standard optical depth of one (i.e.  5000Å = 1 ).