Is brachydactyly due to mutation?
You are correct that brachydactyly is a dominantly inherited disorder and is usually caused by mutations in the BMPR1B gene.

However, not everyone who has the mutation, will have clubbed thumbs (the phenotype). This is due to a phenomenon known as penetrance and expressivity.

Penetrance essentially is an all-or-none phenomenon whereby certain individuals who have a mutation express the phenotype (in this case, clubbed thumbs) and some do not express it at all.

Expressivity is when individuals who have the mutation, will express the phenotype to varying extents. For example, only one thumb may be clubbed.

I hope this helped.