The LEF input as shown in your attached picture, is in fact a RCA input connector.
The "Subwoofer pre out" will output the LFE channel as long as in the RX-A2070 speaker setting you set the subwoofer 1&2 to "normal" (see owner's manual page 126)
He was correct but only if you set the RX-A2070 subwoofer setting to "none". If you want to add external subwoofers, then you obviously have to set the subwoofer setting to "normal", so in that case you have to use the "LFE Subwoofer Input", and connect it to the RX-A2070's Subwoofer pre out (use either one with a splitter in order to feed the left and right BP8020ST.
Yes, that is the right way to do it if you want the BP8020ST to receive the LFE channel, otherwise skip it as suggested by everetT. You can try both ways to find out which way sounds better to you. Skipping it would likely get you flatter bass response though.
Edit: I just noticed your room seems too big for 1 or even two PB1000. If two PB2000 exceeds your budget then you probably should get one (the PB2000) for now, and keep the option to add a second one later.