How to choose verb after "there" in beginning of sentence?

Cambridge "Advanced Grammar in Use" provides following rule in Unit 95C:

If the noun phrase consists of two or more nouns in a list, we use a singular
verb if the first noun is singular or uncountable, and a plural verb if the
first noun is plural:

• When I opened the fridge there was only a bottle of milk, some eggs, and
  butter.


• When I opened the fridge there were only some eggs, a bottle of milk, and
  butter.

But Grammar Girl in episode 278 Oddness When You Start a Sentence with
"There Is" gives completely different explanation:

A listener reader named Joe wants to know whether he should say, "There is a
couch and a coffee table in the room," or "There are a couch and a coffee table
in the room."

...

It's a compound subject since it has two nouns connected by the word "and,"
which makes it plural ... Now that you know the subject is "a couch and a
coffee table" and that it's plural, it's easy to choose the right verb:
"are."

I'm somewhat confused by these contradictory rules. Could someone explain what I'm missing here?