You can pay taxes in us and tell Hungary that you are paying taxes in US

The answer is NO, the US corporation or US Business is taxed on worldwide Income. US Corporations or US based businesses do get foreign tax credits for money that is payed to countries outside of the US to be reported on the US Income Tax Return. The office in the foreign country should be able to set-up and report any and all tax related issues in that country, and keep the US based parent company informed of any and all issues and activities. US has tax treaties with almost ALL nations across the globe and generally have a good way of sharing information between each countries tax authorities And they have the agents and abilities to track assets and income worldwide. I have this information due to the fact I am a Former IRS Revenue Officer

While you are subject to U.S. tax laws, it is very difficult for the IRS to grab wages or assets located outside of the United States. Some countries, mostly in Europe, have treaties with the U.S. in which their tax agencies can cooperate with the IRS to collect from U.S. citizens, but most governments place a very low priority on working these kinds of cases. You may also owe taxes to the government of the country where you reside. Some countries give you credit for taxes you pay to Uncle Sam; others won't. Also, estate and inheritance tax laws vary widely across the globe. The best way to get an answer pointing directly to your question is through a Hungary businees site/forum or someone that had experienced the same issue like yours.

That would depend on Hungary tax laws; this forum mostly deals with US Tax laws. I would contact a competent CPA in Hungary to give proper tax advice.