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:
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 diodemostly due to the internal resistance of the diode, 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.