>But at the end of the day, if you're hiring an outside company to do this, why does it matter to you what language it's written in? Shouldn't they be able to use their best tools?

Unless the owner wants to be forever betrothed to the outsourcing company the language selection is a valid concern. For instance, [she|he] may want to take over updates when iOS9 comes out and plans on being proficient in Swift by then.

The owner should weigh why they wanted Swift in the first place vs. the consultant's recommendation and then decide from there.