You’re probably right about not needing the RAM/swap data. All the data you need for a restore should be on the filesystem, with the exception of any caching going on with the database.
The problem with taking a snapshot of a “live” system is that the data can change while the backup is happening. For example, if the backup gets halfway through the database, and then something changes, the backup will carry on regardless. But when you go to restore, the database file will probably be corrupt.
I think other cloud providers will have exactly the same warning - Digital Ocean certainly does.
The way Discourse deals with this problem for its own backups is to put the database in read-only mode, and then use the database’s built-in backup methods.
The only real way to put an entire operating system in “read only mode” is to shut it down, hence their recommendation.