They don't need to be present to make the request, but most of the banks I've dealt with would require them to pick up the documents "in person" and show their LEA credentials upon delivery. Some banks also require a letter from the agency indicating the person is authorized to pick up the documents.
The fact that your bank need not require a subpoena does not suggest that you can mail, e-mail, or fax customer information based on a phone call. They're not ordering a pizza...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.