Sampling orthogonal signals
I'm afraid that your premise is wrong. The Fourier transforms of two orthogonal signals do not in general have disjoint support. You know that two signals $u(t)$ and $v(t)$ are orthogonal if

$$\int_{-\infty}^{\infty}u(t)v^*(t)dt=\int_{-\infty}^{\infty}U(f)V^*(f)df=0\tag{1}$$

where $U(f)$ and $V(f)$ are the Fourier transforms of $u(t)$ and $v(t)$, respectively, and $*$ denotes complex conjugation. One possibility for (1) to be true is indeed that the product $U(f)V^*(f)=0$, but this is of course a sufficient condition, not a necessary one.