Absolutely always ask for the old parts back. No, they cannot maintain a parts bin full of hundreds to thousands of used parts for each of thousands of vehicles so they have somebody else's used part to give you as a trick. In rare circumstances that is "possible" but bordering on paranoia more than likelihood the majority of the time.
You should ALWAYS ask for the old parts back. Even if it is someone else's part, what have you lost by doing so? Absolutely nothing, and in some cases, that may even make them reevaluate their diagnosis because they didn't want to replace the part that they knowingly misreported as bad, just to tell you that they did and bill for it.
In this day and age it is not that hard to figure out if a part they give you back, matches pretty close if not exact to what it's supposed to look like, but if you're that suspicious of a shop, don't take the vehicle there in the first place, or if it's driveable, tell them you need to wait to do the repair to accumulate money, then mark the parts with a chisel, stamp, or marker, etc so you'll see if what they give you is what was on the vehicle.
Lastly, we don't even know if there's anything wrong with the rear bushings. If they are taking perfectly good bushings off one person's vehicle and handing them to the next person as "old parts back", that's evidence they've screwed two different people rather than only one. Any evidence at all is better than ignorant trust of someone willing to charge you $800 labor for what will probably take them 2 hours to do.