I hadn't seen that clip from Los Angeles Daily Herald but I had seen the one about the train trip from Fresno to points East [which, oddly, does not mention Arthur although I know that he was traveling with his parents at the time]. I don't know why it says they were arriving from "the Colonies." I guess that means Hawaii. In fact, the Logans were arriving from New Zealand but probably came via Hawaii.
In late 1879, the Logans had moved from Pohnpei down to the Mortlock Islands to take up missionary work there. By the end of 1880, Robert was seriously ill and he and his family were evacuated from the Mortlocks to New Zealand in July 1881. They stayed there until Robert was sufficiently recovered to travel to the U.S. - they left Auckland at the end of January 1882. They stayed in the U.S. until mid-1884, sailing back to Micronesia from Hawaii in July. Beulah went back to the islands with her parents but Arthur stayed in the U.S. for about a year [attending school in Ohio??] and then he returned to Micronesia in 1885.
It seems clear that Beulah was with the family before 1882 and probably since 1877 so the only real question is, was she adopted? Probably not, but it is curious that my grandmother would have gotten that wrong. She was pretty careful.
I can recall my grandmother mentioning Beulah in conversation but at the time I had no idea who she was and was uninterested in her or any other ancestor. If I had shown any interest as a child, this wouldn't be a mystery now.