That's close, but it's not quite complete. There seems to be lots of confusion here, and that's natural: It is confusing.
For just-getting-power from a USB A port into a USB C peripheral: There are supposed to be 2 resistors in the peripheral device [always], and also 1 resistor within the cable for USB-to-legacy cables[1]. That's 3 resistors, total, to get a relatively dumb USB-C equipped peripheral device to reliably charge from both USB A and USB C hosts/chargers/whatevers:
The cable itself: It gets an internal 56k pullup resistor between Vbus and USB C pin A5 -- which is the CC line [yes singular]). This resistor signifies the capabilities of the host/charger/whatever for devices that care (some do care, some do not care).
The peripheral: This minimally needs two pulldown resistors [commonly 5.1k], between each of CC1 and CC2 [yes a plurality] and ground[2]. This tells a compliant USB C host/charger/whatever "It's OK! Send the juice juice!" regardless of connector orientation.
[1]: https://www.usb.org/sites/default/files/USB%20Type-C%20Spec%... section 3.5
[bleh]: Again, it is a confusing thing. Nobody said that dealing with such flexible, ambidextrous connections would be simple. CC performs a lot of different tasks: It can be a bidirectional serial bus for active PD negotiations, and/or a resistor network for passively dealing with power, and it's the bit that performs detection of cable orientation for applications where that matters, and it probably does other stuff too.
That single little wire is clever AF. It'd be simpler to use multiple wires instead of just one, but that would take more copper. Copper is expensive, and we each save a tiny bit of money (or a large pile of money globally) by using less copper instead of more of it.
My point, which matches what you've written out in more detail, is that there's supposed to be stuff (resistors) in the cable, stuff which is often not there. There are plenty of these abhorrent cables in the wild. And when you come across one, things get weird, because some sources and sinks deviate from the standard in ways that make them work with these bad cables. Others don't do that. (I believe there were a lot more abhorrent cables in the early days, and thus began the chain of accommodation....)
So unless your cable is known-good, if you are having trouble, trying a different cable should be the first thing you do. It really does often get things working.
Contrarily, if you have identified a naughty cable, it should be immediately widlarized.