As has been pointed out, it is not 'socialism' but it is a significant step towards socialism. And yes, free universal education K-12 is also a significant step towards socialism and is a good indicator as to how 'free' college would change our graduate education system in America. I have only a couple friends who went to private school as a kid, but I know lots of people who went to a private college. Many of the private colleges will close when people have the option of going to school for free vs paying everything themselves.
Rather than looking to take what has worked really well in America (capitalism) and applying it towards parts of our country that need significant improvement (health care, education, etc), a large group of people seem to want to take the worst parts of our country (a grossly oversized government at most levels) and apply that to what needs fixing. The inevitable result will be a complete shit show that will spiral to the parts of our country that work well like the relatively free market economy.
It is easy to see how people label things as 'socialist' that are not actually socialist in and of itself, but will take a significant step towards socialism when taken to their logical conclusion. You are correct that the ACA is not completely socialist, but it is trending our health care system away from free market economics towards the socialism end that many seem to desire.
The ironic part of military members speaking in support of things that point towards socialism is that the military is about as socialist as you can get in America. How many times do you speak well of the MPF, finance, or similar things in the military? Virtually everything that is broken in the military is a great example of what our country as a whole would look like under people like that lady. Having lived in countries with socialized medicine and governments that lean far further socialist than ours, I can tell you that absolutely nothing of that style of government will help us. Government and bureaucracy is both naturally inefficient and naturally self interested in getting bigger and more control. The bigger and more control it gets, the more time, energy, and wealth is wasted simply maintaining it.