Wells Fargo and Sallie Mae aren't the only options for ATP (or any other flight school). They are simply two options ATP has chosen for convenience. You can use any reputable lender or, if you're lucky, the proverbial rich uncle.
Now, as far as getting into debt, it isn't necessarily a bad thing. Everyone's financial situation is different and so is their debt tolerance. This is where thinking ahead is vital. Your primary focus is to make sure that you can service said debt while also taking care of the day to day stuff (living expenses, etc). In short, learn to love Ramen.
ATP quotes "earn up to $42k/year" working as on of their CFIs. This figure includes the "up to $11,000 in tuition reimbursements" figure. Not all airline partners offer that amount and not all participate in any sort of tuition reimbursement. The key here is to assume you'll make the rock bottom amount as a CFI. Last time I did the math (about a year ago) that figure was about $28k ~ 30K per year. With that in mind, and with help from my family, the math worked. Your situation might be better, or worse. There is no one size fits all answer here.
Bottom line: unless you are independently wealthy, there will be some "belt tightening" needed to pursue professional flying.