Grace, I also find this distracting while reading. I've not read the article at the link, nor do I know of a more succinct summary, but of the two examples you noted, the ones with the dialogue set off by commas are incorrect, IMO. They go against everything I ever learned. The clauses set off by the commas in between the pieces of dialogue are complete sentences showing action, not someone speaking, and are therefore not dialogue tags. They should be punctuated as shown in the examples with the periods. The only thing that should be in a sentence of two pieces of dialogue set off by commas are the actual dialogue tags, such as "he said" or "she said" (or anything else actually implying speech - asked, exclaimed, etc.).
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Fast is fine, but accuracy is everything. ~ Wyatt Earp