I am assuming that your folks separated during the RIF in the 90's. It was a unique time, and some were offered VSP (voluntary) aka Palace Chase, which is probably what your folks did.
2 decades later, I am betting this is not about paying back anymore, because typically they only had to do 8 or so yrs like any reservist, AD members, even pilots only owe 11 yrs.
That being said she is correct. When the 92 RIF came about anyone that commissioned in 85/86 as an AFROTC cadet was on the chopping block. 95% in that yr group with a AFROTC commission was cut. None of them had control of their fate. We knew several that were handed walking papers, and some of them had just received a Silver Star from Gulf I. Some were in Weapons school.
They thought they were safe. They weren't.
Bullet's yr group was completely safe, and not only that 5 yrs later O4 promotion boards were sped up, and rates increased from 60-80% because they had gutted so hard the previous yr groups, they needed more in his. On top of that although from the day he entered in 88 for UNT, there was always talk of this yr they were going to give a WSO (aka CSO) bonus, in 03 they finally did because again, they cut so many out of those yr groups their manpower needs were short and they had to offer a bonus to keep the experienced WSOs.
The point is a lot has to do with timing. Had he graduated 1 yr earlier he probably would have been cut. As much as you think coloring within the lines you should be fine, I get your folks fear because there are so many things out of your control, and in the control of AFMPC's control, which you can't predict.
Quick question what is your AFSC goal? This could be their fear. It is a double edge sword.
Say flying, and your folks know that statistically many will not wing, and the AF can cut you loose if you bust. Non-rated and another 92 RIF the AF can/will cut a non-rated in your yr group over a rated. A rated costs millions to train, and can slide into being a maintenance officer and still bring experience into the field with limited financial expense. The same can't be said for sliding a maintenance officer into a cockpit.
People tend to forget that the AF has a defined budget, and operate like corporations, regarding finance, goals, missions, and man power needs regarding long term strategic planning.
You can't predict the future, but all I can say is as a parent, listen to them, have a plan B in place and think 1 step ahead at all times for the what ifs. If you can illustrate you get the what ifs, and have a path for that, than your folks will love your decision. They don't want you to endure the pain they endured. I am guessing if it was 92, and you are 19, by the time they had to leave, you were born. That is scary as a parent of a newborn, believing all was right in the world, and turned upside down less than a yr. I understand their fears.
Congrats on the scholarship. The best is yet to come!