Actually just read that Obama quote again:
“we obviously have a deep interest in making sure that one of the closest allies we will ever have remains a strong, robust, united and effective partner”
If the United States truly believes it has a deep interest in making sure that Scotland does not become independent, we can be quite certain that America will be pulling out all the stops to make sure that No wins. The language is the language of intelligence service tasking memoranda, which Obama is consciously or unconsciously reproducing. I have personally been involved in a great deal of intelligence service tasking. Intelligence service resources, both personnel and financial, are deployed to a greater or lesser extent to a task according to an assessment of the depth of national interest involved. If Obama has decided the US has a deep interest in the result of the Scottish independence campaign, we can expect hidden interference at Ukrainian levels.