Very low mileage diesel would worry me as they need to be driven to stop them clogging. How many miles has she done?
Would also be a little nervous with no service history, engines are good, but like most cars need to be serviced regularly.
When you say cosmetically lacking, what does that mean, does the exterior/interior look like the low mileage.
Car may be perfect, but what you describe would trigger some alarm bells to ask more details. If car has been serviced by jaguar franchise, may find service history online through Jaguar, my entire service history is on their system.