It may well be the cause. However, while both of you are using measures of normal development, they are not absolute. An infant instinctively grasps and tries to put what it grasps (usually someone’s finger) into their mouth.
It is conceivable that a two month old would touch and grasp some object that could cause the injury.
However, such an event is unlikely to go unnoticed, the baby immediately screaming in surprise and pain.
Probably a fissure split - but the immediate assumption of parental guilt is what bothers me.
The first assumption should always be that the parents want to care for their child properly; until proven otherwise. Good outcomes are more likely to result from working with the parents under this assumption to correct any problems or deficiencies.
Taking a child away from the parents can be deeply traumatic, and too often it seems to be done in a spirit of governmental self-righteousness instead of a spirit of help.
Grasping an offered finger within the infant’s reach is not the same milestone as picking up an object and placing it in the mouth (that is more typical behavior of a four month old).
Sucking on an object within reach is a reflex behavior common to two month olds. Focusing on an object, picking it up, and bringing it to the mouth is not.
Any object a two month old could grasp would have to be explicitly offered by an older child or adult. Were that the case, since the couple in the story seem honest, they would be likely to tell the doctor “Older child gave Baby a _______ before we could snatch the object away. Baby started gumming the _______, which cut baby’s tongue” than to lie about it.
Ainsworth proved this but apparently some social workers are lagging in education.