Hello, two things:

1. Typo in fist line of section Alternative method
If you are currently running JIRA 3.7 or later, you could simply connect your new JIRA to your old database (see Connecting JIRA to a database), and let JIRA attempt to updatee the database schema.

2. Rewording of section Alternative Method
from this:

The alternative method will not work if you are upgrading from 3.6.5 (or earlier), as JIRA 3.7+ cannot automatically update older schemas. If you are running JIRA 3.6.5 (or earlier), and cannot use the recommended method of XML backup/restore, you will need to update the pre-3.7 database schema by hand before proceeding with the alternative method.

to this:

This alternative method will not work if you are upgrading from 3.6.5 (or earlier), as JIRA 3.7+ cannot automatically update older schemas. If you are running JIRA 3.6.5 (or earlier), you should use the Recommended Method as outlined below.

If for some reason you cannot use the recommended method of XML backup/restore, you will need to update the pre-3.7 database schema by hand before proceeding with the alternative method.

Reason:
Many customers get confused with the wording, for example:

I am attempting to upgrade from Jira 3.6.5 to 3.11. The upgrade path outlined on your website strongly recommends backing-up our data and then performing each incremental database upgrade before bring up the 3.11 application.