synology: rsync via ssh requires full path

I found the following behaviour on a Synology RS814+

> ssh backup01 rsync
Permission denied, please try again.

> ssh backup01 'which rsync'
/usr/bin/rsync

> ssh backup01 'echo $PATH'
/usr/bin:/bin:/usr/sbin:/sbin

> ssh backup01 '/usr/bin/rsync'
[... rsync version and usage information ...]

Who can explain this?