Question on database backup

We have customers who prefer to use their backup facilities
instead of what we provide in the app (we use pg_dump)
I hear speed is at least one consideration.

The questions I need to answer are these:

1) Is this absolutely safe to do file copy (cpio, or
smth. else, whatever the robust backup app. would use)
on the Postgres db, when it's completely shut down.

2) Same question, but the database is up and running in
read-only mode. We're making sure that no updates are
taking place.

If it matters - this is on Solaris, HP, Linux.
We're using v.7.3.2 running on UDS and v.7.3.4 on TCP/IP
We provide no explicit settings for wal, fsync and the like.
And (yes, I know) they often install it on NFS.

Thank you much.
Mike.