How does the Free Freighter quest REALLY work in No Man's Sky?

The first time the player completes a freighter rescue mission in No Man’s Sky they are given the option to obtain said freighter for free. If the freighter is not accepted, this option is carried on to the next rescue until the player finally accept – from that point onward, any new freighter must be bought normally.

Given this is an one-time offer, most player try to use the "free freighter" option to obtain one of the two "Capital" models (Venator / Sentinel) and just stick with it. Multiple tutorials exist to guide players in the process to acquire their preferred ship for free, usually listing a process similar to the following.

• wait until the next warp will trigger a freighter rescue battle.
• SAVE BEFORE WARPING
• warp to a new system. Look at the freighter – if it is one you don’t like, reload the save and go to a different system.
• if the freighter is the one you were looking for, do not save it yet. Go to the system space station, perform a quick save, reload the save and exit the station.
• every time you reload the quick save and exit the station, the battle will be triggered again. This allows for "easy" freighter class scumming (every time the battle is triggered, the freighter gets a random class, so it is possible to redo the battle until you get an "S" version).

Things get a little more fuzzy when one is trying to get a capital ship. The available guides usually don’t fully agree on the required steps.

• some claim that the first freighter is always a regular one but if you refuse it the second offer is guaranteed to be a capital one
• some claim that you can get a capital ship on the first offer but only in three star economy system (normally, an higher economy level means the system offers rarer ships)
• some claims that the first time you are offered a free freight the number of inventory slot is capped to 19 and that in turn doesn’t allow capital versions to spawn (since the worst capital ship would still have more than 19 slots)
• some claim that the real caveat is that the first rescue mission is offered at about 5 warps but capital ships requires at least 8 warps, so they are not yet unlocked when the player get their first rescue mission (but extreme speed-runs may be able to bypass this limit since there is also a minimum total-playtime requirement that may allow players to get to the required 8 warps before their first battle).

I have passed the point where I can test this in my game, but recently a friend was asking me for some hints about this very topic. Since they don’t have access to portal coordinates yet, they can’t just use the Coordinates Exchange archive to go to system that has the ship they like. For that reason, I was trying to make sense of the various theories, but couldn’t find a definitive answer.

So, I am asking if anyone here can link a source that backs up its claims with actual data (maybe from datamining the game logic or quoting word of god / patch notices).