Your DD has a unique opportunity. I agree that the choice is not the same as "big state U with no loans vs. U.S. private school with $150K in loans". If I were in your shoes I'd be inclined to want to make it possible.
Some things to consider:
Is DD your only child, or have you/will you be funding other college educations? I have two daughters, and while I've never worried that "fair" = "spending the exact same amount of money", I believe it's fair to keep the spending somewhat equal. If taking on large loans for DD means that a younger sibling will have limited options, I wouldn't do it.
You say you cannot afford to pay the extra $50K per year but can afford the loan payments. Is it just a cash flow problem, or will the loan payments adversely affect your ability to run the household/save for your retirement? I would be adverse to so much debt but I don't know the details of your finances.
As far as the posters advising your daughter should get her own loans, that is not likely to happen. Student loans in the US are limited to $5,000-7,500 per year for the student. (I don't know if Stafford loans are even available for students attending college in another country). Additional private loans are available, but someone will need to consign for her. What bank is going to lend $50,000 to an 18-year old student with little income and no assets?
Disclosure, because our experience colors our opinion: DH and I paid about $250K (total) to send our two DDs to college for their BS degrees. There was no need-based financial aid offered, and we were able to pay by using savings and current income. There were no loans.