Prepositional Phrase can act as an adjective to modify a noun , or as an adverb to modify a verb.
for the stated example, the prepositional phrase is modifying the noun "Kelly", and it can be rewritten as:
Mr Kelly, according to committee, had recorded Jim's statement in a memo.
I am not an expert, but throughout my studying, I don't recognize a reference saying that prepositional clause could modify a whole clause.
Participial "verb-ing" type clause is the one modify a whole clause.
I remember an exiting example:
"hopefully, my plane arrived on time"
outside the GMAT, this sentence seem correct, as "hopefully" is modifying the whole clause.
but inside the GMAT, this sentence is incorrect because the adverb "hopefully" can only modify a verb, which is "arrived". since the plane cannot arrive in a hopeful manner, the sentence has a meaning problem.