How far does the word "COSTS" go?

[LandoC 1]

I saw a FAQ for the Port District battlefield saying that if you decrease the cost of a card being played below 3, or play it for free, then it does not gain ambush.

This begs the question, how far does the word "COSTS" go?

If I spend 1 resource along with It Binds All things to reduce the cost of a Lightsaber attached to a Padawan, then can my opponent use Disarm & remove a die showing 1 ranged to remove that LS?

Or, if I spend zero resources along with Reaping the Crystal & It Binds All things to reduce the cost of a Lightsaber attached to a Padawan, then can my opponent use Rend to remove that LS?

There are MANY instances where this word "COST" or "COSTS" can come into play regarding discarding supports & upgrades.

Examples: 

Reduced cost cards:  Doctor Aphra, Armored Reinforcement, Black Market, Destiny, Lukes Training, etc.

Affecting cards:  Confiscation, Disarm, Rend, Dismantle, First Claim, Sabotage, etc.

Thoughts???

[Atomisk 66]

I think this is covered in the playing a card rules post but my take is that cost is the static number on the card. Reduction effects only apply during the timing window for actually playing a card, but don't affect the card outside that timing. The problem with Port District is that it checks the cost at the time it's played.

[Mep 2,291]

Yeah, there is no memory of what something actually cost to be put into play after that action is fully resolved. So disarm will always hit the printed cost. This also goes in reverse, so when you have to over pay for a weapon, like K2S0, disarm is still the printed cost, not the paid cost.

[kingbobb 159]

There's been debates on this in the past, and I haven't seen a solid resolution in the RRG.  Cost as a term is not well defined in Destiny, although there's not really a lot of debate as to what it means, just a few corner cases that start to get murky when you look at them too hard. 

Essentially Destiny uses "cost" as a term to mean a variety of things, mainly:

The printed cost of the card
The Resources you pay to play the card/resolve the die (which would be better referred to by something else, like "price"