Ct scans with contrast are used either to track veins as described here, or with oral contrast, to check the digestive system. X-rays are used to detect broken bones. A CT with contrast to check for broken bones makes no sense.

Med student pede here, but the typical protocol for diagnosing a stress/hairline fracture is x-ray first, then MRI if you really need a diagnosis but the x-ray is negative (although that's pretty uncommon given how expensive they are).

I've personally haven't seen CT scans being used to diagnose broken bones very often (given how much radiation they use), and current guidelines say that they aren't recommended for hairline fractures because they have a high false-negative rate. They're only recommended if you suspect extensive bone injury, which doesn't seem to be the case here.

There are some studies that suggest that CT and MRI have comparable diagnostic accuracy, so maybe Biden's doc just went with the faster option. CT scans are also more liberally used for older patients since the risk vs. benefit of getting cancer isn't a huge concern when you're nearing the end of your life.