Full disclosure: I'm a rising senior at Stanford, so maybe your comment is just irritating to me on a personal level. That said, the Stanford CS department is objectively very good; further, judging by the number of people I know who have abandoned or failed out of CS here, plenty of people wouldn't be able to complete the coursework for the undergrad degree even if they were all enrolled. I agree that hiring people based on their school is bad practice (see: people failing out of CS), but I don't think it's fair to call any engineering degree a "pretty piece of paper." I've put too much work into mine for that.
Ability to complete coursework is not necessary and sufficient for being a good engineer in a company. Sorry. I've seen too many people flounder around, never completing things, making inane suggestions, and so on, all while talking great theory. Of course, I've seen the opposite, and Stanford is a very good school, I don't think anyone would deny that.
And that shouldn't be surprising. Look at brilliant physicists. Most end up in either the theoretical or experimental side, and are often quite bad at the other. Likewise, theorem heavy CS has its place, but getting through a program like that doesn't mean that you can write a for loop (I've interviewed Stanford grads that fumbled and failed though that), design readable, robust software, push through a sea of decisions and make effective, near optimal decisions (the whole SW life cycle is a n-dimensional optimization problem), get along with peers, and so on.
There is a huge cachet attached to degrees from certain institutions that really isn't deserved, in my opinion. In that sense the paper is "pretty". It's not a slam of the effort anyone at is undoubtedly making at the school, but the reverent regard with which it is regarded.
Except that's really all it is. You might be fancy with your degree for a short period of time and land some interviews others might not, but it soon all goes out the window. The second you have some sort of industry experience, where you went to school and how you did there doesn't really matter.
Your "pretty piece of paper" is essentially like getting your drivers license. It allows you get behind the wheel, but it makes no guarantees you'll be any good at driving. In the end it really doesn't matter much which DMV you go to.