@Avik. First of all, I will say straight away that It has been about 20 years since I learned these halachos.
Also, you are arguing nuance, when my point is that technically, most jews have a chezkas kashrus.
relying on what you wrote, there is an inherent issue, which you appear to recognize. Specifically, even according to your definition, you need two male frum halacachic witnesses to testify before a beit din. This does not typically happen.
Also, the non-orthodox wedding is a totally different issue for a host of reasons including that there, you actually need eidim to attest to the marriage. Here, you are discussing when some loses chezkas kashrus instead of obtains marriage. Its different.