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@OzNY wrote:

 My issue is whether or not this should be reported on a 1099-NEC or not. 

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Unless you are issuing the 1099, you really don't need to be overly concerned if it was reported on the proper form or not. 

Report the income on the appropriate place on the tax return, based on the facts.  If you believe it should be "other income", then report it that way.

If you believe it is "other income" and not a business, then you will need to decide if (a) you want to report it on Schedule C than 'back it out' for a net result of $0 profit, or (b) tell the client to expect an IRS notice and help them respond to it.

I do think that there are some situations that hosting an Exchange Student could be a business on Schedule C, but other situations where "other income" is correct.  But I don't know anything about your client's situation, so I can't give any input on that matter (you'll need to decide that based on the facts-and-circumstances).