Video host URL different in full content page links than in View links
The solution was to install the Dev version of module Image Link Formatter (7.x-1.0+6-dev). It now seems clear, this module (the current recommended version) was invisibly rewriting the URL, as there is no other way it could be specified to be rewritten in the standard interface options for the content type's fields. Although there was no documentation found for this issue in the issue queue or in documentation about the Dev version, apparently it is a bug that was fixed.