That said, it's a further misunderstanding with utilizing such tools in general. Unique is neither good nor bad on its own. The next question is "always the same unique because that's all you share or always unique because certain fingerprintable attributes are randomized over time/visits/sessions". I.e. it's a war between trying to fake an average enough fingerprint and trying to track someone through partial matches, not just a matter of "is the fingerprint unique".
those systems probably don't even rely on fingerprinting for those decisions - you just can't deny someone acceess to a service because "they're unique", you're opening a can of worms.
entities that do deny access based on fingerprinting actually do it based on same fingerprints corresponding to a marked visitor (like checking behaviour and marking all subsequent visitors with that fp as bad) - but it's a headache.
what you describe usually has more to do with your IP (range, usage type, country), your useragent or added/modified headers (check any extensions that do this)
i had exactly this happen some years ago when i added a `'` in the UserAgent to test a site for SQL injection and forgot to remove it.
I started getting those more often when I moved 2 years ago and switched from Charter cable to AT&T fiber. The same hardware was transported 2 miles away...