Leafy vegetables are short duration in terms of consumption because leaves are harvested again and again with short intervals. Accumulated of NO3 and NO2 cannot be converted into organic forms during this short duration. 

I agree with Nazir's view  

Nitrate content also varies across the plant: leaf > stem > root . Most common vegetables are in the medium range for nitrate content (100–1000 mg kg−1), including peppers, garlic, potatoes and carrots at the lower end, and green beans, cabbage and turnip at the upper end. Vegetables notable for their low nitrate content (

Good explanation by Amin.

Good points by Dr. Nazir, it is true that leafy vegetables are ready to harvest after 15 -20 days interval intermittently at short period does not contribute significantly for converting NO3 and NO2into organic forms. 

If there is high values of ammonium and nitrate in the soil the issues with high nitrate will be worsened. The use of tissue analysis can confirm the status of plants and fertilization practices can be adjusted. Generally when compost is used for growing leafy vegetables they seldom have the very elevated levels of nitrates in leaves. Raw manures and ammonium nitrate fertilizers are much worse in elevating nitrates than compost. The soil analysis is also helpful in gauging the appropriate levels of feeding. High nitrates can develop in shallow wells and particularly in infants with alkaline gut reaction toxic nitrogen metabolism will lead to blue baby syndrome. Nitrate in water in North America tracks with nitrogen fertilization of the maize crop. Nitrate can affect pregnant women and in areas of high water nitrate the incidence of spinal defects are elevated. When analysis is used the rates of fertilization can be modified to avoid not over fertilizing. Considering the issues with fertilizers and raw manures the use of raw manures can be used with strawy compost to produce a complete amendment which is not overly elevated in soluble nitrogen.