In your example, you are correct in observing that "had recently been" would be the appropriate verb phrase following "said." Although "has been" might be used in reported speech after "said," in a sentence like this (not from an obituary)--
Sources said that there has been a lot of recent activity, and that more can be expected –
it is possible only because there still could be more activity. Certainly there was no possibility at the time the obituary was written that the deceased Elvis Presley would ever again be a heavy cocaine user, so "had been" is correct and logical.
"He is survived" is correct. It is a passive form of "survive," and does not refer to the past. "To be survived by xxx" refers to one's descendents who are still living.
"He had two brothers" is of course correct.
If there were rules especially for obituaries, they would indicate that all the verbs about the deceased would be in one of the past tenses, except for the headline, which would read like this: "xxx Dies at 87..."
Here are snippets from obituaries:
"¢ Bob Hope, Master of One-Liners and Friend to G.I.'s, Dies at 100...Bob Hope, whose mastery of the comic monologue and the topical wisecrack carried him from vaudeville to Broadway musicals and then on to worldwide fame as a radio, film and television star of the first magnitude, died on Sunday at his home in Toluca Lake, Calif. He was 100. (The New York Times. July 29, 2003)
"¢ Johnny Cash, Singer Known as 'The Man in Black,' Dies at 71 ...Johnny Cash, a towering figure in American music spanning country, rock and folk and known worldwide as "The Man in Black," died Friday. He was 71....Cash had been released from the hospital Wednesday after a two-week stay for treatment of an unspecified stomach ailment. ...Cash had battled a disease of the nervous system, autonomic neuropathy, and pneumonia in recent years... (The New York Times. September 12, 2003)