I have never seen an asymmetrical tread which was not also directional, but I have to concede that such a thing might exist.Asymmetric tyres are not the same as directional. Asymmetric means they have an ‘outside’ and an ‘inside’ which will be very clearly marked on the wall of the tyre. It is completely wrong to say that asymmetric tyres can’t be swapped left-right - the outside is still on the outside.
Some asymmetric tyres are also directional - in which case that advice would be true. These too will also be marked clearly on the sidewall, with an arrow indicating the direction they need to roll in. These are the tyres you can only move front to back. Don’t confuse the two types. Also, not all directional tyres are asymmetric. They are two completely different properties of the tyres.
I have seen symmetrical tyres which were directional - my last car had those.