The following solution to this problem has been suggested by Lindsay Davies, the author of the BBedit HTML extensions.
Set the Utilities HTML extension preferences to Root directory. The problem will no longer manifest itself.
Additionally, Lindsay suggests the following:
"One suggestion though to make the most of these two tools. Set up the prefs (Root folder, server address, and path), and create a document using a BASE HREF. This will allow you to use all the addressing methods (full, root, and relative). Relative addressing will default to the root address if no BASE HREF is present."