I think (sorry didn’t have any source … even if I am french ^^) that the rule have "wiggle room" for situations where the individual in the group use other things than their thing.

Something like :

Les cochons grattent leur groin. (mean that each pig scratches his own
snout)

Les cochons grattent leurs groins. (mean that the pigs scratch
the snout of the other pigs)

Singular is mandatory when there is a single object related to all subjects, e.g.:

Les français soutiennent leur équipe.

Plural is mandatory when multiple objects are related to each subject:

Les enfants rejoignent leurs parents.

When there is a one to one relationship, like in your example, you are free to select either the singular if you want to insist on the singularity of the object, or the plural if you want to insist on the large number of objects.

Les cochons fouillent avec leurs groins.

Les cochons fouillent avec leur groin.

The trend seems to be using the plural in that case: