From some comments by the OP,
An "intersection" would require a look beyond the EH, I am only claiming that both worldlines "meet" i.e. "touch" at the EH [...] the worldlines of Alice and Bob are approaching each other - spatially - when approaching a point at finite distance on the event horizon, and we know that they will effectively reach the EH within finite time.
This is a misunderstanding. Consider ordinary $(1+1)$-dimensional Minkowski spacetime with line element $\mathrm ds^2 = -\mathrm dt^2 + \mathrm dx^2$, and consider two objects $a$ and $b$ following the trajectories $x_a(t) = t$ and $x_b(t) = t+1$. Their trajectories look like this:
Presumably you agree that (i) these worldlines never touch and (ii) nothing particularly special is happening at $t=1$. However, now I will perform a rather odd change of coordinates, in which I define $u = x e^{-1/(1-t)}$ for all $t<1$. On the patch of spacetime defined by $t<1$ and $|x|<(1-t)^2$, this is a perfectly valid choice of spatial coordinate, and yields the line element
$$\mathrm ds^2 = -\left(1- \frac{x^2}{(1-t)^4}\right) \mathrm dt^2 + \frac{2xe^{1/(1-t)}}{(1-t)^2} \mathrm dx \mathrm dt + e^{2/(1-t)} \mathrm du^2$$
If we now look at $u_a(t)$ and $u_b(t)$, we see something interesting - namely that the two trajectories appear to be converging at $t=1$.
This seems to fly in the face of the claim made above. The trick is that this apparent convergence is not real, and is an artifact of our strange choice in coordinates.
If we had started by using $(u,t)$-coordinates then this would perhaps not be so obvious. However, note that the metric components diverge as $t\rightarrow 1$, which is indicative of a coordinate singularity; on the other hand, coordinate-independent scalars (such as the Ricci scalar, which is obviously $0$ here) do not diverge at $t=1$. Furthermore, observe that the fact that the coordinates are getting closer together does not mean that the objects are; indeed at any fixed $t$, we see that
$$\mathrm ds = e^{1/(1-t)}\mathrm du= dx$$
and so the distance between $a$ and $b$ is the same for all $t<1$, despite the fact that their $u$-coordinates are getting closer together.
My intention here was to demonstrate that we must be careful how we interpret statements made at the level of coordinate charts. In the Swarzschild spacetime, the standard Swarzschild coordinates $(t,r,\theta,\phi)$ have a coordinate singularity as $r\rightarrow r_s$, and exhibits the same symptoms (limited domain of definition, divergent metric components but well-defined curvature, etc) at the event horizon as my toy model did at $t=1$. Choosing a coordinate chart which isn't singular at $r_s$ - such as the Eddington-Finkelstein chart - makes it clear that the worldlines of two infalling objects will not intersect at the event horizon.
