Looks like Canada thistle. If so, your neighbor is correct about the root system.

A careful session with digging and/or herbicides need not also kill the junipers.

Part the shrub branches adjacent to one of the thistles.
Place stakes to hold it juniper branches out of the way.
Cut down the thistle, then immediately paint the cut surface of the stub (in the ground) with a broadleaf herbicide.
Repeat as needed.

Likely to require several years of close attention - every time you see greenery, repeat cut & paint episodes.

This post was edited by jean001a on Fri, Jul 5, 13 at 13:51

Oh gosh, I hadn't even thought about staking the juniper branches to keep them apart while I work. I will try this and get to work on those thistles. Thank you Jean!