I would place Ichigo's dad in the fallen Shiba clan. I don't think Ichigo's similarity to Kaien should be so easily dismissed. Not to mention Kukaku's willingness to help and her lack of surprise it the similarity. I don't even have to mention the lengths Yoruichi went to in order to help him. Isshin's connection to Urahara and Ishida's dad particularly (shown in this present arc) bring me to mind of Kukaku's statement during the Soul Society arc that since Uryu was involved how could she say no.
I would even go so far as to guess that all these past events and connections played a part in the falling of the Shiba Clan from the Noble Houses. However I don't believe that Ichigo is royalty to anyone but his inner hollow (the horse who refers to him as his king).