Yes, see How does solder mask layer work?.
Logically, for “cover everything with mask” an empty gerber file should do the trick (but as we know, it doesn’t for some uncomprehensible reason).
To uncover everything you can just draw a zone with minimum width: 0mm. Why a zone? Because if you have proper edge.cuts lines the filled graphic zone fills the board area exactly.
In any case you should give extra note for the manufacturer in the way they recommend giving notes. They just don’t seem to understand non-common cases which leads to endless back and forth email conversations.
Probably you should also heed the tip from bobc and others by drawing something in the mask layer even if you would like the board to be covered with mask. It seems that you can’t have everything. But exposing some copper with text in the mask layer looks pretty cool. So, if you have a copper zone there, try adding the name & rev etc. information there. Letters can be as small as 0.5x0.5mm WxH, 0.08mm thick, or maybe even smaller.