I think I answered my own question -
catholic.com/quickquestions/are-non-catholic-marriages-valid-in-the-eyes-of-the-catholic-church-what-if-a-catholi
But, the question still remains - can any person, man or woman, layperson, marry two baptized Christians and the marriage is still valid? What constitutes a valid marriage?
Yes, if they have no impediments (too close blood kinship, a previous marriage with a living “ex”), if their church accepts it (the Orthodox Church wouldn’t) and the marriage is legal.
Jo Blow down the street can’t witness the vows of two people and it be accepted as a valid marriage UNLESS he is licensed to perform marriages. (There is the rare situation where these 3 would be in the middle of the jungle with no hope of coming up with a ‘licensed’ person within a one-month period where the requirement to be licensed might not apply but those situations are few and far between.)
But it’s easy enough to be licensed. I know a man who became licensed just so he could be the presider at his daughter’s wedding. AFAIK, he had no interest in witnessing marriages on a regular basis, just that one.
A valid marriage is one where two people with no impediments vow in front of witnesses that they are freely giving themselves to each other, intend to be faithful, married for life and to accept children should God bless them with some.
For non-Catholics, baptized or not, that can be witnessed by a minister, a justice of the peace, a judge or the captain of a ship if they meet the ‘offshore’ requirements.
For a Catholic, this must be witnessed by a priest or deacon or, in rare instances, a lay person appointed by the Bishop with Rome’s permission. A Catholic marrying a non-Catholic might be able to get a dispensation from canonical form to marry outside the Church and have that marriage witnessed by a non-Catholic minister, judge, etc.