I'm working on nearly the same circuit, and am equally confused.
I've seen two classes of designs:
(1) The oscillator manufacturers suggest using an inverter with a large resistor as feedback. Some split the resistor into two halves and add a filter capacitor to ground between them, providing a more stable load to the XO.
(2) Others use a high-speed comparator. For example the HP 33120A and 33220A frequency reference inputs do this. I don't know about other instruments.
For my use, low jitter is not important, so I'll use an inverter with feedback. The different between the datasheet (V_IH - V_IL) isn't so important, and does not need to be more than the peak-peak of the input. This is because the inverter actually has a very small (V_IH - V_IL). The datasheet's values are guard-bands due to process and temperature variation.
This website from Johns Hopkins has a nice image showing the threshold voltage variation of different devices.
The inverter in the circuit will self-bias to hold the input at very close to the threshold voltage of the inverter with the 0.8 Vpk-pk input being larger than the actual (V_IH-V_IL) of the inverter.
Note that Schmitt trigger inverters should not be use since they have hysteresis often > 1V. Comparators with Schmitt trigers are reasonable since they usually have hysteresis much less than the input's pk-pk voltage.