There has to be an article before singular countable nouns, right?

Question

I've gone through the tutorial about "A/an and the" from English Grammar Today in which I guess I understand the rules.

Regarding singular countable nouns, the tutorial states

We only use a/an with singular countable nouns

We can use the with singular and plural countable nouns

The tutorial does explicitly claims something like

there has to be an article before singular countable nouns.

However, in practice, the statement seems to appear to be a rule. Is my understanding correct?

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This is the precise version, which is waiting to be reviewed.

"Usually, there has to be a determiner before singular countable nouns that are not proper nouns"

Answer 1

We do only use "a" before singular countable nouns. The word "a" means "one" and so it implies the noun is countable and singular.

a cat

There could be other types of determiner:

my cat
which cat?
that cat

and so on.

If you are willing to accept proper nouns as "singular and countable", they often can be used without any determiner.

John

or words like "winter", "school"

You can argue that these are not "singular countable nouns".