Buying a used motor may also be more cost-effective, once you factor in the cost of labor as well as of any parts you'll need. When my engine needed replacing, I estimated the cost both ways, and found it would cost less to replace my engine with a used one than to rebuild it. (Note, in my case, it was a stock engine.) Don't forget to include all the costs when estimating - the cost of parts or the engine, shipping costs (which can be significant for shipping an engine cross-country), and what you may get back if you sell the block or other parts from your blown engine.
One other point on the costs (and this applies to a rebuild as well as a replacement) - unless the timing belt and water pump are new, you may as well get new ones installed at this time, when the engine is out anyway. (And consider new cooling system hoses as well.) This will save you most of the cost of the timing belt job, which you then won't need for another 6 years or 90K miles.
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The following answer is not intended to apply to this specific incident, but rather, for any incident in which a car incurs mechanical damage.
The car owner is usually responsible. If the shop admits that their work and decisions caused the damage (or played a role in it), they may pick up part or all of the cost of the repair needed to restore the car to its previous condition. If the owner and the shop disagree regarding whether the shop caused the damage, you can try to work together to come up with a solution you can both live with, but if you can't, you can take it to court. Hopefully that happens only as a last resort and you can work something out.
In my experience, as long as both sides are reasonable as far as understanding how it happened and the work that needs to be done, you can figure out a way of handling it; typically the owner still pays for most of the repair but the shop provides some relief (discounts) on the labor rates, parts costs, etc. This is how I've seen it handled most often.
