There is no case where adding another plane-stitching via will make things worse from an RF perspective. The more your board looks like a monolithic slab of copper, the better.
What can cause problems is inadvertent construction of a parasitic filter structure through overly-consistent via placement. That's hard enough to do on purpose, and not likely to happen by accident. If you think it may be happening, scatter a few more vias at random, and/or create multi-rank fences of vias with different spacing characteristics.
I would simply refine the first sentence:
There are cases where it may: for example, a trace crossing an inadvertent cavity, formed by top and bottom ground pour and unlucky placement of vias. If the signal in the trace is, say, 5GHz, and the cavity's resonances are 3 and 9GHz (give or take, plus other modes), then adding some vias in certain locations could raise the resonance to 5GHz, causing a null in that trace's response.
So, that said, there may be cases where a
dubious design gets worse from more via stitching. But there is no case where an
already-good design gets worse.That is, the cavity / waveguide resonances can only be pushed to higher and higher frequencies, by adding more vias: once all modes, in all locations, are above the highest signal harmonic frequency, the design meets the minimum requirement for stitching.
(Stitching can still be improved from there, because leakage occurs between regions, even below the cutoff frequencies of those regions. This manifests as electric or magnetic coupling -- field leakage -- in the near field, or evanescent (internal and surface) waves, in the far field.)
I can think of another case where it would get worse, but it's a special case: using the ground return path as series inductance. For instance, in a switching inverter, the series inductance to a MOSFET source pin can be used to limit dI/dt and set the switching loop impedance. If the path is intentionally made long, the inductance can become useful (1-100nH is pretty practical).
These sorts of things are better implemented using explicit planar inductors, or net bridges, rather than being drawn in copper purely by coincidence. Because, consider what would happen to your perfectly tuned design, if, down the line, a less experienced layout guy modifies it -- "oh, this ground is flapping in the breeze, let's stick some vias in there, that'll surely make it better!" -- and then it blows up emissions at 300MHz or something!

Tim