You are pretty right.
In case if PE1 receives a broadcast from any other PE (say PE-2) which is a part of same VPLS domain (i..e LDP peer configured) , it doesn't replicate because this is the job of PE-2 which already has LDP full mesh enabled for VPLS (In case you are using Martini Based VPLS). In case you are using Kompella style VPLS (that used BGP for VPLS singalling) full mesh like LDP is not required.
And In case if PE1 received broadcast , multicast or Unknown Unicast from Attachment circuit (or CE) it replicates to other PEs with which it has LDP full mesh signalling configured.
Since you are using H-VPLS, So I am attaching a snapshot from the book 'MPLS Fundamentals by Luc De Ghein' that will help to clarify your query.
!H-VPLS