One Wald interval is based on a standard normal approximation. The interval is

phat +- z_alpha/2 * sqrt(phat*(1-phat)/n)

Another Wald type interval may use the t distribution with a penalized degrees of freedom. That may be what you have seen. Since these approximations are based on distributions that are continuous from -infinity to infinity, the confidence interval can include values less than 0 and greater than 1. You are correct in thinking that it makes little sense to report a confidence interval for p that is less than 0 or greater than 1. These approximate methods were developed to make calculations easier. However, with advances in computer science, it is much easier to calculate exact confidence intervals.

The exact method always produces a more accurate confidence interval. One exact method (derived by Clopper and Pearson. 1934) is:

LBp = y/(y + (n-y+1) * F(alpha/2, 2*(n-y+1), 2*y))

UBp = (n-y)/(n - y + (y+1) * F(1-alpha/2, 2*(y+1), 2*(n-y)))

Where y in the number of successes and n is the total number of trials. F(a,b,c) is the upper 1-a percent point of an F-distribution with degrees of freedom b and c.

~Matt