The reason this function doesn't escape double quotes is because double quotes are used with names (the equivalent of backticks in MySQL), as in table or column names, while single quotes are used for values.
This is important to remember, especially coming from another SQL implementation. It can cause strange problems, for example, the query:
SELECT * FROM table WHERE column1="column1"
Would actually return every record, because column1 is always equal to column1. This should instead be:
SELECT * FROM table WHERE column1='column1'
Double quotes are not escaped by the function because they are not interpreted specially within single quoted strings.