Why Does A Brønsted–Lowry Acid Accept Proton from Stronger Acid?
Nitric acid is definitely a strong acid, but that does not exclude the possibility of protonating it with a stronger acid. It can be effectively protonated by a stronger acid such as sulfuric acid. Simply because something has "acid" in its name does not mean it has to dissociate into protons and its conjugate base, or protonate something else. 

$$\ce{HNO_3 + H2SO4 &lt;=&gt;H2NO3^+ +HSO4-}$$

Note also that even strong acids in their pure forms - i.e. liquid nitric acid or liquid sulfuric acid - can and do auto-ionize to a fair extent. So if nitric acid can react with itself, of course it can react with a stronger acid.