If the software is ran from your own machine it is not cloud software and it is misleading to say it is
Adobe doesn't say that it is "cloud software". Creative Cloud is just a marketing term which you failed to understand.
The real question no one has answered is will Adobe say no to these entities?
If you're worried about it, just don't use that feature. The same applies to Dropbox, Google Drive, or any of hundreds (thousands?) of other online storage services. To use this as an argument against subscription service is nonsense.
If you are at the end of your 99 days and you are unable to validate your license
You're really working very hard to invent reasons not to subscribe. It'd be easier to swallow if you just said you don't like it and left it at that.