Boreas said:
Okay, let's talk about that.
Let's say that there is a n event that says "after you lose a challenge, pay 1 gold to take the bottom card of your discard pile and put it into play an Army character with 4 STR, a mil , an int, a pow icon, and deadly." What is the "printed STR" of that character? The effect that created it and defined the parameters is not only not printed on the card that is acting like a character, the card that did define the parameters isn't even in play anymore. But its 4STR was printed somewhere, so doesn't it still count as the printed STR by your earlier line of reasoning?
Or what about Dagmer Cleftjaw, who says Warship locations you control count as 2STR during Dominance? Does that mean Warship locations have a printed STR during Dominance? By the logic you present, the 2 STR they have during the Dominance phase is a printed STR, even though it is printed on Dagmer instead of the Warships.
Or let's look at Summer Reserves as is again. What happens when I put Milk of the Poppy on it? Does it stop being a character? Does it stop being an Army? Does it have no STR, icons or keywords? The answer to all of those questions is "no." The effect that turned the event into a character has already resolved. It does not depend on the continued activation or presence of the event text (any more than the presence of the hypothetical event in the first example is needed) to maintain the definitions of its "character parameters." It's the lasting effect that matters, not the printed text - once it has resolved. So you see, what is printed on the card isn't actually what has any bearing on the character's parameters beyond the initial resolution.
Hopefully, these examples demonstrate that just because printed card text in an effect defines a STR for a card (even when it is not gained) does not create a "printed STR" for that card.