There are typically two valuations of private companies. The "internal valuation" is usually the valuation of the common shares (ie, those that are granted to employees) whereas the "external valuation" is the value of the "preferred" shares that investors purchase. The external/preferred valuation is usually higher because the preferred shares have more attractive terms (such as that you get your money back first before other equity holders are paid out).
From the article: "A 409A valuation is an independent estimate of a startup’s fair market value often used to price stock options to employees."
I don't think it's as nefarious as that. What people are calling the "public" position here is the value of preferred stock sold in a financing, and the "internal" valuation is the value of common stock. They're different things - the preferred stock has downside protection and other special rights that make it more valuable than the common stock so it should have a different price. These internal valuation reports pretty explicitly calculate the value of the common stock as a discount applied to the preferred stock price, due to the rights and liquidation preferrence and the fact that the common is not freely tradable.
From the article: "A 409A valuation is an independent estimate of a startup’s fair market value often used to price stock options to employees."