Hydrolysis of salts containing amphiprotic anion
If the degree of ionisation is equal to the degree of hydrolysis, then (assuming you take the same initial molar concentration of [HCO3-]):

Let's say the initial concentration was 'c' (with no [H2CO3] and no [CO32-]), the degree of dissociation to be &alpha; and the degree of hydrolysis to be &eta; 

At equilibrium:

[CO32-] = c (1 - &alpha;)

[H2CO3] = c (1 - &eta;)

Since we know &alpha; = &eta;, we can say that [CO32-] = [H2CO3] 

Only because you made the assumption that degree of dissociation = degree of ionisation, do you get pH = 7.

But, since we assume water to always be in excess, even in a real-world situation, difference in pH (from 7) would not be significant.