my parents owed me money when I went to college
I love this, but only on paper. In reality, I'm sure it wasn't fun for anybody. But as an idea, it's fun.
I'm one of those who thinks an emergency fund has to come first, for the very reasons you describe. I advocate a smallish emergency fund to start, then debt repayments, then a bigger emergency fund. (I'm a big believer in the Dave Ramsey approach to kick-starting life.)
The whole owing-me-money thing wasn't fun, no. I can do a wonderful walking-uphill-in-the-snow-barefoot type story. To this day, I have no real idea how much was borrowed from my college fund, or if it was all paid back. I was declared independent for purposes of financial aid, though, which helped a lot.
For me, I wanted a larger emergency fund. It's not that I'm risk-averse -- it's that I'm overly risk tolerant, and wanted to learn to make myself do better. Also, one of the biggest helps was watching the interest in my ING account grow, and it helps to have a fairly large balance for that. However, when your highest-rate debt is only 1/2% higher than your savings, you have a lot more leeway than if your debt is at regular usurious credit-card rates.