What causes both components of a binary gas mix to condensate at the same time for a given composition

Okay, so recently I encountered the temperature - mole fraction diagrams for binary vapour-liquid equilibrium. For now, I only consider two-component systems where the components are very similar and form ideal mixtures, e.g. a 50:50 mix of Benzene and Toluene. 


I understand it from the liquid to vapour transition side (i.e. increasing T) and can do the calculations required, but when I start with only vapour (high T) and cool the mix I am confronted by the following problem: 


A vapour component can only be in equilibrium with its liquid when it's partial pressure is equal to the vapour pressure (P\*) of the liquid - or in the case of mixtures its reduced vapour pressure (Raoult's law: pi = xi.P\*).


What bothers me is that the partial pressure of the less volatile component at the dew point is still lower than the vapour pressure of its pure liquid and with no liquid present (yet) there can be no mixing which will lower the vapour pressure. Yet both components condense.


Possible explanations I could come up with include:
A bit of less volatile component condenses and as it has similar properties, small amounts of the other component enter solution (almost like Henry's Law for solubility of gases). This affects rates of evaporation and condensation until equilibrium is reached.


Does this make sense or is there something else happening here?


