Meagher–Spiga intersection-density conjecture for prime-product degrees

For a transitive permutation group $G$ of degree $n$, let $\rho(G)$ denote its intersection density, and define

$$\mathcal{I}_n:=\{\rho(G)\mid G\text{ is transitive of degree }n\},\qquad I(n):=\max\mathcal{I}_n.$$

Intersection-density conjecture for prime-product degrees. The following assertions hold:

1. If $n=pq$ where $p$ and $q$ are odd primes, then $I(n)=1$.
2. If $n=2p$ where $p$ is prime, then $I(n)=2$.

These assertions would determine the maximum intersection density in two families of degrees. The paper cites them as conjectured previously; no resolution is supplied in the given text.