You are right. I have found the most recent version of the German rulebook. It clarifies this in several places (and shows the translation is inaccurate). The translations provided hereafter are my own work.
Description of Abilities (Page IV)
Zu Beginn von Phase D (Ende
der Runde) kannst du eine Infektion mit
Glück (würfeln) und/oder durch Erfahrung
(Abgeben eines BP-Plättchens) heilen.
At the start of Phase D (end of the round), you can heal a trauma with luck (rolling a die) and/or with experience (discarding story points).
The notable point here is "and/or".
Picture of Character card Charles (Page XI)
Du kannst (würfeln), bevor du nach Infektionen
schaust. Wenn du 5/6 erhältst, entferne eine
Infektion von einem beliebigen Spieler. Du darfst
2 BP ablegen, um eine Infektion von einem Spieler
You may roll a die before checking for traumas. If you get a 5 or 6, remove one trauma from any player. You may discard 2 story points to remove one trauma from any player.
Note how there is no conjunction here. It simply puts each possibility into its own sentence, implying they're not dependant on each other.
For reference, here's my original post which pointed out why the conclusion would have been different if the translation had been accurate.
Let's take this text apart:
You may roll a die before checking for trauma.
Checking for trauma, as you said, can only refer to the check whether injuries will become traumas, which happens during the End of the turn phase. Before performing this check, you may roll a die.
If you get a 5 or 6, remove one trauma from any player.
That's pretty self-explanatory. You choose any player and remove one trauma from that player. Unless you rolled 1-4, in that case you don't.
Then, you may discard 2 story points in order to remove 1 trauma from any player.
I think this is where the confusion really starts. "Then" in this case could either refer to "After rolling and potentially removing 1 trauma" or to "After successfully removing one trauma". It really comes down to interpreting this "Then".
Unfortunately, the official rulebook gives no hint as to how it is to be interpreted except (Page IX)
IN CASE OF DOUBT
Castaways is a game with many options, and while we try to clarify all of the interactions
between the cards, sometimes there is some doubt about how they should interact. In
these cases, we recommend that the players use common sense. If that is not enough,
you have the option of taking sides and performing a strength roll.
Common sense (this is reflected in several other card games) dictates that "Then" is only applied if whatever was supposed to happen before did actually happen. This is more obvious in cases such as "take a shower, then put on some clothes, then leave the house" and less in cases such as "eat something, then do the laundry", but still usually applies. If you're told to do "A, then B", unless you can do A, doing B is either obsolete, unwanted, or impossible.
If you were to do the last part even if the roll is unsuccessful, it should read something like "Also, you may ..." or "Additionally, you may ..." or even "After trying, you may ...".
To conclude, the clear text should read
During the End of the turn phase, you may roll a die before checking if injuries will become traumas. If you roll 5 or 6, remove 1 trauma from any player. Then, if you do, you may discard 2 story points in order to remove 1 trauma from any player. This skill can be used once per End of the turn phase.