I believe that in D&D play a character is established as not having an item if it's never brought up that they have acquired it. This would be another unspoken D&D principle. There can exist a few exceptions (an NPC planting something on your character and being unaware of it till later). So in D&D if you didn't establish having an item, then establishing that you had it the whole time would be a retcon in D&D.
That said, BitD is a different game with different principles. I don't believe it's fair to talk about BitD using D&D principles. In BitD there is no principle that if you don't establish having an item that you don't have it - the rope makes a great example as it's something allowable by the rules.
IMO it's the mis match of principles (especially unspoken D&D principles) and game rules that often gets us into trouble when comparing different RPG's. For you I think it's important to understand this is what's happening as it may help you better communicate with D&D players that don't realize they are mismatching D&D principles with other games that don't share those principles when they are describing such rules and play with negative words like retcon.
Let's unpack this.
You're saying that there's an unstated D&D principle by which it would be bad play for a player to suddenly remember, after leaving town, that they had wanted to buy something, ask the GM if it's okay, and the GM to say sure, go ahead and mark it. I don't think this is true, and I'm pretty sure you're not going to blanket claim that this cannot happen or is not supposed to happen ever in D&D. So let's look at what might be the reasons:
1) timing. If the player is making the above request when said item is useful, this feels bad. So timing is a problem.
2) permission. The above is okay because the GM is permitting it.
For 1, this seems artificial. The problem here is that we're assuming that since the player didn't think of it, the character cannot have thought of it. Even if the fiction had the players planning the mission, and the possibility of a use for the item was discussed, using the above timing makes it not fair because the PLAYER didn't do the right thing. We already elide huge amounts of what characters do (unrealistically so, in D&D) and do not follow every step. We allow for this in many other parts of the rules -- no training to improve abilities, no need to take actions to gain new spells, etc. So, timing is already a rather large hole in D&D. This argument is either about the need to challenge the player in their logistical abilities or it's special pleading that this isn't the usually accepted place to ignore timing.
For 2, this is about authorities. The idea that the player might have a certain number of 'I don't need to ask permission" slips to bring in the item is the problem.
For the record, because I know a good number of you have no idea how Blades does loadout, but the fiction is that the PCs have done thorough planning for the mission, but we elide that at the table. The players pick a level of loadout -- 3 items, 5 items, or 6 items (light, medium, heavy), that have consequences (light doesn't look like you're up to no good, medium looks like you're up to no good, heavy is call the bluecoats, this guy's loaded for bear). During the score, there is a list of commonly useful items for skullduggery that you can check loadout boxes to have brough with some requiring multiple boxes (like a heavy weapon requires 2, or armor requires 2, and heavy armor requires 3 more past that (total of 5)). If you want something special, you had to have either "acquired an asset" previously or you need to do a flashback to acquire the asset (which raises the cost of that and you don't know the quality of the asset you'll get until you roll, so more risky). That's the loadout system in Blades. Very tightly constrained, but no GM permission needed. Mimics the detailed planning that goes into a score and that fictionally has already occurred. Bazookas are not on the list (but, in hack where they could be, they'd already be accounted for in the balance of the system and would not be an "I win" button).
Also, it needs to be said that items will rarely just win a situation (and almost always in that case it was a good acquire an asset prior). They provide a different opportunity. Like, thugs accost you, and you spend load to pull out some knives so you can more effectively fight them. Or have a rope to increase the effect of a check to climb a wall. The crazy assumptions about how these things work are exactly what you complain about when you say, " I don't believe it's fair to talk about BitD using D&D principles." That's really only happening in one direction, here, because I run 5e, I know how it works intimately, and, even given all the times you've been involved in these discussions, you still show that you do not understand how these other games work.