Their "no outside association" rule violates labor law. They may say it's about workplace romance, but it also prevents union organizing.
They're not allowed to prevent union organizing.
This is a blatant violation of 29 USC 157. Read it.
You engaged in "concerted (together) activities", "for the purpose of" "mutual aid". Yes, really.
It doesn't matter whether you discussed labor organizing, all that is required is that you might've. Anyway, your meeting certainly was about employees looking out for each other, which is the very seed of union organizing. And that isn't any of their business anyway, you don't need to justify that by telling them you're labor organizing, in fact they're specifically not allowed to even ask, or otherwise snoop on your “whatever it is that might be labor organizing".
Really. This conversation isn't allowed to even happen:
"you were fraternizing with Kalpana outside of work. Reprimand! Read the handbook."
"Kalpana and I were labor organizing".
"Oh, that's all right then, reprimand canceled, by all means carry on."
No. They don't even get to ask what you are doing, because they are not allowed to go on a "fishing expedition" in the neighborhood of anything protected, because that itself would have a chilling effect. They would have to confine their inquiries to the topic of something they could reasonably prohibit.
What to do
ASAP collect for yourself two copies of the employee manual. Write down, as soon as you can, an accurate retelling of what happened in the meeting, and go have it notarized to capture the date. Keep and treasure a copy of any written reprimand they gave you; it's worth its weight in gold.
Why? You can use it to build a case against the company for violating labor practices. First, you'll use it if you are subsequently terminated in a way which might relate to this matter: at the very least, to defend your right to collect unemployment, as they will say you are not entitled since you were terminated for cause. Second so you can contact lawyers and pursue a wrongful-termination lawsuit.
In at-will employment, they can fire you for any reason or no reason at all, but not protected reasons such as race, religion, sexual orientation or many other categories, and association with workers outside work is one of those categories. However, this is a "self-help" area of law: you hire a lawyer to go after them, and the lawyer is typically paid on contingency (free until you win, then they take 1/3). This payment method makes them a "fire and forget" weapon, you do not need to ride herd or micromanage your case. You can also seek any legal aid societies your government provides for free.
Even if they do not fire you, you may have recourse, and that is worth talking with a lawyer right now. Their reprimand was also wrongful.