No one is claiming that she never attended Standford, they're claiming she never earned a degree from Stanford.

Well, "alumni" implies you graduated, implies you earned a degree.

The correct answer is that that "Alumni card" is for the MFP (Mayfield Fellows Program), a nine-month program within Stanford that gives you some entrepreneurship experience. The alumni card is for that program, not Stanford itself.

No, or at least MIT counts me as an alumni despite $$$ preventing me from graduating.

That said, I only claim to have attended and done well, not graduated.

That is definitely the general assumption as it's most often true, but university alumni associations don't hold to that, nor do dictionaries.