Does negative reference evapotranspiration make sense using FAO Penman-Monteith equation?
Short answer, especially if it is about 1% of the time series and these values are just slightly negative, this likely indicates that the ET needs to be recalibrated slightly, and for practical purposes you can set the ET on those days to 0 mm/d. The ET calculations typically calculate potential ET, meaning that if there is no water available no ET will occur, and a similar concept applies to negative ET values (i.e. no demand for water -> no ET).

A couple of notes 
- the reference $ET_0$ calculations were meant for ten-day or monthly time steps, not daily, which may be a reason for these results (see top of Ch 2) 
- the equation seems to be for a specific type of reference grass, and they suggest adjusting the $ET_0$ based on crop type using a ratio; another potential adjustment to make

Overall if the negative values are infrequent and close to zero then likely setting to zero is not an issue, if the values are much less than zero than check the calculations and try the suggestions above to recalibrate the calculation.