Frye is a legal standard of evidence, the lowest of which is the opinion of an expert. That would be superseded by test data, and ultimately by proof.
With foundation movements, it is impossible to go back in time to monitor moisture change in the soil below a basement so absolute proof does not exist for a specific basement. It has been shown to occur in research.
A expert can look at a structure, in a area known to have high swelling soils, note the trees, perhaps some wetter areas near downspouts, and if there is a correlation with distance from a major tree and the amount of shrinkage, that is the floor points to a tree, it is likely that shrinkage is to blame. It it point up at a drain spout, or a source of water, swelling is likely.
Now to remove doubt, one step at a time. First to demonstrate the soil has swelling/shrinkage potential. There is a good correlation between Atterberg limits, a index test for classification, and swelling. That only tells us that the soil is capable of swelling or shrinking. Add some moisture tests, and we can know that it is within the normal range that shrinking and swelling occurs. When we have condition that is dryer at the tree, wetter away from the tree, for similar soil and strata, the data would suggest that the tree is drawing water from the soil. But all trees draw water from the soil, and most draw more adjacent to the tree than away. This can get altered where there is a drain spout at the tree. Ideally the best demonstration we ever get after the fact, is a high plastic soil, and higher moisture contents at the high points of the structure. A range of moisture can usually be established.
There are odometer tests, where a "undisturbed" sample of soil is placed in a testing apparatus, the height measured, it is saturated, loaded, in steps over time, and allowed to swell, consolidate, rebound, and the results are analysed. But usually the soils in the field are not saturated to start with, so it tells more about the soil and its potential than what actually happened.
Now for the complication. Lacustrine deposits are varved, that is there is a variation in the clay/silt ratio with depth, often varying 40/60 to 60/40 in a few inches, or a foot vertically and be visually indistinguishable. The Atterberg limits, moisture content, hence the swelling potential, and the moisture holding capacity also vary. Comparing the moisture's without Atterberg limits on each sample is little better that an option mixed with some test data.
Now if we do four testhole, to 12 feet, with 12 samples per testhole, do moisture on all samples, limits on all samples, at about $100 each plus sampling, logging, field time, you have a nice bill, for a better suggestion of the possibility. Some of that data will be meaningless, or misleading, so what to do, we ignore some of the tests. Suppose we do four testholes to 12 feet, a sample/foot , moisture on all, and say 4 limits on selected samples. Now we are introducing bias of the geotechnical engineer who is selecting the samples to conduct limits on, unless we say something like even testholes at foundation level, odd testholes at 1 foot below foundation level. Then it is biased by the person selecting the testhole order or locations.
The location must be selected to show the range, 2 in the dry areas, 2 in the wet areas. Ideally for a house, we would like two in the high area, two in the low area. This may mean 2 inside, and two out. To make matters worse we may may looking for 2 percent difference dryer hole to wetter hole, when over a few inches, the soil may vary 4 percent vertically in one testhole, so "proof" is not always obtained. The suggestion may be there in the data, or perhaps not. So now we can have a question as to what the data really shows.
One testhole in a area expected to be wet, at a downspout not near a tree, and one near a tree, not near a downspout, can be the best demonstration variability, with moistures every 1 foot, to 3 or 4 feet below the foundation may be advisable and a few limits just below the foundation level.
Now testholes on private property requires two liability wavers, one from the home owner and the insurance company we are working for must be willing to pick up the risk of a unknown utility strike. All known utilities can be located, both public and private, and avoided. This assumes that locations are available and accessible.
Next is the other issue, the method. Inside is hand work. Coring through concrete floors is messy. Hand auguring below is tough work, and requires a skill that must be trained into people doing manual work, as well as myself to observe, and a junior engineer to sample and log the testholes. This all assumes that there are suitable locations to conduct testholes. Where the house is surrounded with trees, the outside testholes can be a issue also. Finding a "wet locations" that is clear of utilities is not always obvious, and close to the house. The front or rear lawn, well away from the house is often the only choice. Close to a tree, or within the same from the tree as the house is is often the best available choice for the "dry location".