I've seen a memo from a major EDP vendor (perhaps yours) saying that it is definitely reportable on a 1099MISC. However, they did not cite anything in support of that conclusion. My read was it was a simple CYA memo on their behalf. The fact that yours says "should report" rather than "must report" generates the same reaction from me.
I'm curious as to whether you will get any responses from banks that say they do it, but either way I suggest you tell your vendor you want a citation from IRS resources that says it's required. ("Oral notification" from the IRS is meaningless and the distinction between interest bearing and non interest bearing accounts is senseless.)
The debate on this point is more than 5 years old. So, if the IRS is interested, they would have put something in writing by now.
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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.