The rebbetzins/kosher kitchens you have observed are probably doing full checks rather than "sample" checks because full checks are often required for leafy vegetables.
Vegetables which are buggy a majority of the time, or even a significant minority of the time, must be thoroughly checked. Even checking a majority of the vegetable in question is insufficient, let alone "sample" checking (Shulchan Aruch Yoreh Deah 84:8 - the Rema explains that when the Shulchan Aruch says "Vegetables which are normally buggy must be checked" it means "even if it's only a significant minority of the time").
The question is, how often is "a significant minority"? R'Elyashiv apparently told authorities outside of Israel that they could be lenient until about 15% (heard from Rav Yitchok Berkovits). Rav Moshe Vaye (in Bedikat Mazon K'Halacha) wants closer to 6%. Rav Wosner says anything that would be unsurprising to find - even if it's a tiny statistical likelyhood, 1% or less - requires checking. A common compromise approach is the Shut Mishkenos Yaakov which says 10%.
Kashrut agencies each decide which approach for "significant minority" they will use (which is technically a "minhag" of psak halacha/halachik decision), then must observe how buggy each given type of produce is in their area. There can be major variation even in the same fruit or vegetable based on source, shipment and storage methods, climate, etc., so what is frequently buggy in one place may not be problematic in another. Therefore it is best to follow recommendations of a reliable authority as geographically close to you as possible.
Checking a few random samples as an approach is harder to place a source on (it appears to be related to YD 84:9, but that's not direct), and is suggested by Kashrut agencies in cases when the vegetable in question does not strictly require checking, or it is questionable whether the vegetable requires checking.