If you want to change "their" to mean "data about them" rather than "data owned by them" you have to not give precedence to the original public meaning. The result of that is that ordinary people are in a worse position to know what the law means, because it can fundamentally change by reinterpreting a word.

"data owned by them" is one's papers and/or effects, depending. "data about them" pretty much didn't exist in the late 1700's when we compare it to the enormous scale of that data today. A combination of the third-party doctrine and legal restraints that prevent it from being turned into dragnet surveillance is more or less what applies to that.

There are also the rights of the people to peaceably assemble -both publicly and privately-, peaceably speak publicly, and peaceably bring their grievances to the various governments that govern them. All of those rights interact with regulation of the things we're talking about here... it's not just the 4th amendment that's relevant.