As a work around, I used the exact URL which I thought came from my old backlinks (which I needed to preserve).

And, I set ReDJ plugin to redirect all errors to my home page. That way, any minor variations to the FROM URL will go to my home page instead of to an Error 404 page.

To verify this, set "case sensitive" to true, and check the rule's hits counter when the request should not match (i.e. with lowercase f), the hits counter should NOT change.

I tried this, and the hits counter did not change.
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JSo in your case there must be a different rules that matches when you change the case.

As a test, I disabled all the other rules, but the problem remained. Also, I tried changed the letter case in a browser URL for some other ReDJ redirects, and sometimes it cased and error and sometimes it did not. Also, I tried reordering the redirects in ReDJ, but that did not fix the problem.
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To check the rule applied, just sortfor "last visit" date and check the first one.

I tried this, with case sensitive checked, and with it unchecked. In both cases, the redirect that originally caused the problem remained at the top of the list.
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I have to say that I'm impressed with the support that you are giving. I think I can live with the problem, now that I discovered ReDJ's feature that can redirect all errors to a chosen page (I chose the home page). However, I am very happy to accept your assistance if you think we should investigate it further.