What if, instead, the guy was 100% honest and up front about it, and offered to enroll the Czech guy in all security checks that any other contractor would get, and treat them legally as any contractor would be treated?
I wouldn't see anything wrong with this, but I would be willing to bet that 99% of companies would not go along with it--for reasons I'm not sure I understand.
If they were ok with doing the work to bring in the overseas person in the first place why should they hire their onshore cutout? To do it legally would be a whole mess of getting involved in business in a new country.
The main problem is at that point the US guy is operating outside the model of being a direct employee of the company. He's operating as a contracting vendor.
There's legal aspects to the employer-employee relationship that are different than the company-vendor relationship.
Even reporting the pay to the IRS as personal income would probably be legally problematic, because from a legal aspect a vendor is being paid for a service not an individual receiving income from an employer.
I wouldn't see anything wrong with this, but I would be willing to bet that 99% of companies would not go along with it--for reasons I'm not sure I understand.