Interesting that a speech therapist was involved, because swallowing is in some ways the opposite of vocalization. The larynx goes up and eustachian tube briefly opens. This is the opposite of what you want when speaking.
Many SLPs work in medical and rehabilitation settings, often with older patients. (And indeed, this work generally pays better than school settings.) Swallowing is a major topic, since not being able to do this competently can have fatal consequences.
Beyond that, SLPs deal with a number of practical cognitive issues. Some of these are related to language specifically, others with related processes. If you've had a stroke, you might have severe problems generating spoken language, even though you can still generate written language without trouble. Or, you might have difficulty with basic planning tasks that we usually take for granted (e.g., what exactly do you need to do to mail a letter?).
Additionally, speech therapists are used to working with patients with neurological disorders.