Actually they are still the level they competed. It's pretty simple. Everyone is training for the next level except 10's (some are training for elite) and elites. If it's not an exaggerating parent then why include the qualifying statement "training level x"? I'm not trying to pick on you, I mean this generally. If our kids hear us say this about them, does it sound like level x really isn't that good so we mention the next level?
At my daughter's gym there actually is a formal distinction between the L3 group training L4 skills with the intention of moving up and those training only L3 skills with the likelihood of repeating.
I call my daughter's level what the gym calls it, which coincides with the level the gymnast is competing or will compete in the current year. She will compete L4 this year and is in the official L4 group doing only L4 routines, so it would be weird to keep calling her L3 for the next few months until the first meet. When she was in the L3 group training L4 skills, I called her L3 because that was the level she was competing. It's kind of like school--she finished fifth grade in June, so now she calls herself a rising sixth grader, not a fifth grader.