After watching episode 13, I realize I misunderstood some things.
So far in the anime (up to episode 12), from these three we've seen (if I didn't miss any) only the Stationary Guard's patch.
This is most likely wrong, as we'd seen Levi before, and he belongs to the Scouting Legion. See this image from episode 13:
In episode 13, we also see the Military Police's patch, although from a distance:
The patch is visible on the arms of the guards standing by the cell
This means we've seen all three patches (Scouting Legion, Military Police and Stationary Guard), plus the Crossed-Swords patch.
Now, my misunderstanding came from the fact that the characters I mentioned in the question are listed in the Shingeki no Kyojin Wiki as affiliated either with the Scouting Legion (Eren Jaeger, Mikasa Ackerman, Armin Arlert and Jean Kirschtein) or the Military Police (Annie Leonhardt).
However, episode 13 also shed some light on this matter, when Jean identified Marco Bodt as "The 104th Training Corps Leader of Squad 19, Marco Bodt."
Also on episode 13, Levi tells Eren he'll accept his application to the Scouting Legion:
NOTE: The Scouting Legion is dubbed/subbed as Recon Corps in the anime
This would mean that the characters mentioned in the question still belonged to the Training Corps, and that the affiliation mentioned in their SnK Wiki pages (which, in addition to the fact that I was under the impression they had already "graduated" from the Training Corps, caused my misunderstanding) is, presumably, from the manga, which is ahead in the plot.
Basically, as JonLin wrote in the comment below the question, the Crossed-Swords patch belongs to the Training Corps, and no affiliation seems to have been changed.