Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Spooky.
If she wasn't running a fever and this were my case, then I would want to rule out pancreatitis in a cat this age who has the signs you mention.
As to why this condition might develop, well, we usually don't have a good explanation but it's actually a fairly commonly seen problem.
We do have several tests to help confirm this condition (both an inhouse one and ones which a lab would have to run) but they usually have to be requested as add-on tests; they aren't typically included in most routine chemistries, in other words.
Having said that, though, I've come to doubt their reliability for all patients with pancreatitis since no test is 100% reliable. Routine blood work is often normal in these patients, by the way.
Every vet might approach this condition somewhat differently but I usually treat my patients with fluids and pain medication (we believe the pain is why they stop eating) and possibly an appetite stimulant.
An x-rays isn't going to be terribly diagnostic for pancreatitis; usually an ultrasound will be of more benefit. In my experience, however, most cats this age will respond to symptomatic treatment fairly quickly such that additional diagnostics are not necessary.
It's difficult to justify an x-ray in my opinion in this situation in the absence of symptoms which point to a specific organ system (gastrointestinal, cardiopulmonary, etc) although I suppose your vet is just trying to be thorough by suggesting it.
But, if the blood work is abnormal, then it might make more sense.
I hope this helps and that she continues to improve ...which it sounds as if she's doing. Deb