If your motor had thrown a rod you would most likely have a hole in the oil pan and the motor would probably be seized up. You wouldn't be driving it anywhere.
Your problem could be low oil pressure (caused by a bad oil pump, clogged pickup, clogged/defective oil filter, etc.), excessively worn main bearings. Depending on what exactly the sound sounds like and where it's coming from it could be a number of other things too.
What exactly did this mechanic do? Did he pull the oil pan and find your rod and piston in the pan? Since he's obviously lying about the thrown rod, did he pull the oil pan and remove some bearing and rod caps to get a look at the condition of the bearings and main/rod journals? In any case, you may very well need a new engine, or it could be as simple as freshening it up with new bearings. Since it sounds like you can't do that work yourself, if that's the case the cost of repairing your engine vs. having a rebuilt engine installed will likely be very small. In that case it would be worthwhile to put a new engine in it and be done with it.
Depending on what you paid for the car and how long you plan to keep it you have to decide if you can justify that cost/investment. If you're just going to get a new engine you can drive this one into the ground. Just throw some straight 50w oil at in and see if that quiets it down some until it don't go no more. Of course that's assuming the problem is worn bearings.
The other day my car started knocking loudly at lower idle speeds, it's got a 302 .030 over with ~12,000 miles on it. If I bring the RPM up a little it quiets down, and when I get to more RPM it's silent. I was afraid it was a rod knock, or possibly shot main bearings. Problem seems to be bad water pump bearings. When I hit a deer at 55 MPH a while back the impact made my radiator kiss my fan. After a new fan and radiator the next morning I was back in business. Apparently the impact bent the water pump shaft enough to put a slight wobble in it, and after enough miles like that the water pump bearings got real loose from the stress. That wobbling with the loose bearings seems to be the cause of the knock. As I rev the engine the fan puts load on the bearings and makes enough force to keep the water pump pulley straight. Watching the pulley as I rev the engine the noise gets quieter as the pulley straightens and goes away once it's perfectly straight. This week I'm gonna replace the water pump. Just pointing out an example of how what sounds like a really bad problem can turn out to be a real cheap and easy fix. A new water pump will cost me maybe $30, but I'm expecting to get it replaced for free as this pump has a lifetime warranty. Either way it's not bad.
I suggest taking it to a competent mechanic and having the problem properly diagnosed. Then have him explain to you exactly what is causing the problem, and lay out the options you have to fix it and the cost.
Cory