My initial reaction was much like the OP's position: Healing Surges refers to a game mechanic term in 4E, and for the rogue, any Healing Surge restores 6 plus Con modifier (Stat Mod plus Half Level). It was just my gut reaction when I read it.
I think Healing Surges are triggered by a number of powers, spells or special conditions, such as Second Wind.
I imagine that multi-classed characters will use the highest of their Heroic Surge numbers, or perhaps the Heroic Surge of the class with the highest level (and their choice if they have two or more classes as the same level), instead of an average between the Heroic Surge numbers of all classes.
I think the reason I did not think of them as per-day abilities is simply because I don't recall seeing anything in 4E that says you get to use this resource X times per day, per encounter, or per level. Instead, they are categorized by level of renewal, and it appears that powers work only once within those conditions, unless another game mechanic resets them (like spending an action point, for example). Action points will likely be the only game mechanic that avoids the per day, per encounter, etc. limitations that appear to be presented so far.
Of course, this is only my opinion, as uninformed as it is, and as always, YMMV. I believe we may have some insight after this next weekend, though.
Looking Forward To The News Then,
Flynn