If you call any accountant or small business bookkeeper you will most likely receive an answer through a quick phone call. You also try asking this question on Quora.com - the people that work at HR block (a tax preparation franchise) don't typically know more than what the computer walk-through provides them, they are mostly temp jobs and trained on the job for the tax season mostly. Your best bet is to go to Quora.com and ask. I'm not a certified accountant but I did take accounting classes during my MBA program and have been working with startups and companies in various countries... here is my answer to your question:
I hope it’s not confusing:

Non-residents are subject to U.S. income tax only on U.S. source income, they are subject to two different tax rates. One for effectively connected income (such as wages, self-employment earned in the U.S. or from the operation of business in the U.S.) and is taxed the same way as a U.S. resident. The other taxation is for income that comes from passive income such as interest, dividends, rents, or royalties, this income is taxed at a flat rate of 30%, unless a tax treaty specifies a lower rate. Non-Residents must file and pay taxes using Form 1040NR.

So to answer the question, YES you will have to pay taxes on stock shares received from company #2 since it’s registered in the USA and the income is being reported in the USA.

My name is Humberto Valle, I'm a marketing strategist for http://Unthink.me - we bring big business tools and experts to small startup growing companies. Our facebook page is facebook.com/iwillunthink - I would really appreciate it if you follow me there ;)