The valuation wasn't all that high. It was just twice that of the last round. In order for the investors that just came in to get any sufficient return on their investment, they had to at least double their money. Ignore, for a second, that it was just 1 month (or 1 night as Techcrunch suggests) - it doesn't matter.
The purchase price is usually determined based on the latest round of financing.
The $500m-valuation round happened so close to the buyout, though, that it's quite possible the investors in that round knew of pending offers, which then increased the valuation. So if that round's valuation itself then increased the buyout's valuation, that's a neat bit of circularity.
The purchase price is usually determined based on the latest round of financing.