It's a valid assumption because it's close enough to true that the difference is negligible in many cases. See for example this graph from [LTL-307EE][2]:

![led voltage vs current][1]

Notice that the voltage axis starts at \$1.2V\$, and over the typical operating range of the diode, the voltage only varies about \$0.6V\$. This is [mostly due to the internal resistance of the diode][3], which in this case is about \$13\Omega\$. If you are going to put this diode in series with a \$4.7k\Omega \pm 1\%\$ resistor, then the \$13\Omega\$ resistance of the LED is quite insignificant compared to resistor you've added, which might deviate \$\pm47\Omega\$ from the nominal value of \$4700\Omega\$. Put another way, that \$13\Omega\$ of resistance from the LED represents a \$0.28\%\$ error in your calculations.

  [1]: http://i.stack.imgur.com/1AGbv.png
  [2]: http://media.digikey.com/pdf/Data%20Sheets/Lite-On%20PDFs/LTL-307EE.pdf
  [3]: https://electronics.stackexchange.com/questions/76367/accounting-for-led-resistance/76378#76378