When downloading headers only, usually TB status shows "Downloading headers X of X" which is the first step... then if synchronisation enabled says in a second step "Downloading msg X of Y" but that is not what happened during test related to my previous comment. TB direclty went to download msg and dis-regarding settings. Putting TB offline showef msg were available offline while they shouldn't if sync is disabled on Folder, only available in online mode.
Bug 1733966 Comment 9 Edit History
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When downloading headers only, usually TB status shows "Downloading headers X of X" which is the first step... then if synchronisation enabled says in a second step "Downloading msg X of Y" but that is not what happened during test related to my previous comment. TB direclty went to download msg and dis-regarding settings. Putting TB offline showed msg were available offline while they shouldn't if sync is disabled on Folder, only available in online mode.