Yes. (Though that doesn’t mean they are wrong or misleading in this case.)
Which is why it is wise to look at actual objective nationwide data first. Anecdotes are useful in suggesting where to check real data (or gather real data if missing).
Whoever is gathering supermarket pricing data on a nationwide basis (secret shoppers) would objectively know what’s happening, if anything, and if it is local or regional or nationwide. An actual news agency would have contacted them and paid for the general non-proprietary regional/national info.
I agree with your take on this being a staffing issue where you are, if they are posting those sorts of signs and actively hiring.