We have just bought an Ornithogalum thyrsoides plant and on the plastic label it says "Propagation strictly prohibited"

No idea... sounds very odd!

I understand that some growers are now trying to 'copyright' plant cultivars that they produce. Whether or not there is any legal basis for this or not I don't know.
In the case of your bulbs it is nonsense as Ornithogalum thyrsoides is a natural species and no one can claim ownership. If it was O. t. 'Rodbell Beauty' then there might be a reason for the label, though personally i think the the grower is just being a chancer.

Just to add a point, a grower can take out protected status for a variety of a plant which means that you need to pay a royalty to him/her if you propagate that plant for commercial purposes. There is no legal restriction on propagating plants for your own use.

There was something about this on Radio 4 a few months ago. If I remember correctly, there is no responsibility to prove that they even created the cultivar (although I may be wrong).
It is becoming increasingly common to find this on plants. However, it is still a grey area when it comes to seeds.