Kind of looks like everyone is infected not just had contact huh? Wonder if this one is what is called Battlefield Anthrax. Not good..not good. Genetically reengineered.
"Currently," adverb phrase, modifies "occuring", redundant
"all infections" subject
"are occurring" verb phrase
"within" preposition
"the major-market media community" object phrase, and a monstrousity
":" connective, when two sentences are called for
"persons" subject of new mini-sentence
"at NBC," first clause of a clumsy multiple phrase modifying the subject
"the Boston Globe" second clause of same
"and American Media" trying to be the last of same
"(owners of The National Enquirer, The Star, and The Globe)", adjectival phrase, modifies "American Media", and a true grammatical abomination
"have all fallen" main verb phrase of second half of the sentence, split by an intrusive "all", which modifies the subject, "persons"
"ill" object, what has befallen the subject, clumsy use of conventional construction
"or" logical connective signalling multiple verb construction
"demonstrated" second verb, not even the same tense as the first, should be "have demonstrated"
"signs" object of second verb of second half of the sentence
"of anthrax infection." adjective phrase, modifies "signs"
You are correct that the intrusive "all" in the second half of the sentence modifies "persons", and not "infections" or the named media companies. The "all - or" construction is also terrible. The whole sentence would have Strunk turning White in his grave. Oh, and "sentence" has three "e"s and no "a" - LOL.