Also refer to the following site/thread.
The Difference Between the Particles "wa" and "ga" - 80/20 Japanese
を vs. は | Japan Forum
It totally depends on the context.
は works as the contrastive marker in that case, thus, it means "Alice ate it (but other person(s) than her, including the speaker, didn't)". In other words, Tae Kim's explanation "You can't say 「アリスは食べた。」" is also an example of "countless number of equally confusing (and sometimes wrong) explanations", or at least it's insufficient.