Is this from first hand experience or from the general understanding of how they work ?
Additionally, my friend actually interviewed with another company (wasn't Google or Amazon, but the big one in Menlo Park). He was hired, and they gave him a choice to move to another country as needed.
In general, I think they will try to transfer you to another country. The main issue is that the specific country could be limited, and you might not really have a choice as to which country it is.
However, when you apply to big companies, don't go in saying "I want to be a senior engineer". That means different things at different companies. Quora has some great answers on how the ladders work at the big players; you will see that "Senior" can mean 10+ years of experience at some places. Feel free to send me an email if you want more info about one of the places you mentioned.