But my client has to report the expense somehow, no matter whats the method of payment (could be cash) -- he needs a company name.
That's not true. US companies can pay individuals, requiring at the very most a US taxpayer identification number, sending you IRS form W-9 to collect it.
Any non-US citizen can fill out IRS form W-7 to get a US taxpayer identification number.
And getting a US Tax ID number is not even needed in many cases.
For example, in almost all cases personal services performed by a non-resident alien and outside of the United States are NOT subject to US taxes because personal services are tax based on source of income and in that case are not US sourced (See IRS website).
At most the business would collect a W-8BEN(-E) and have a reasonable belief the independent contractor is performing the services outside the US (perhaps a signed statement to that effect, etc.). This would be extremely defensible record keeping for the business.
People interested in these two areas should consider learning the lay of US law by reading Secrets of Independent Contractors and A Lawyer's Take On Bitcoin and Taxes.
In this case, it really sounds like frisco2's client does not really understand how tax and reporting requirements apply. Involving another corporation merely to invoice is unnecessary and overly complicated for adequate tax planning to engage in legal tax avoidance (in contrast to the illegal tax fraud or tax evasion) and ironically will likely create greater tax liability than would otherwise be due. But not understanding the labyrinthine rules and regulations is pretty common and a reason to read the two short guides on the topic.