It has been a reasonably common thing for those to be false codes. It has happened to my car several times. The cats are not bad because it easily passes a smog test with readings near zero.
It has been common enough that Ford has published a TSB to reprogram the PCM for some Contiques (mine not included) that widens the parameters for settig the codes.
First of all, make sure you are up on your maintenance, such things as spark plugs, air filter, oil change, injector cleaning, throttle body cleaning, and possibly the intake cleaning using the vacuum suck method. If there is ANY question about the UPSTREAM oxygen sensors, replace them. Reset the light by disconnecting the battery for about five minutes (or removing fuses 4 and 11 in the fuse panel under the hood) for about 5 minutes. Drive the car long enough to clear the P1000 code (monitors not run) and see how you do on a smog test.
When you take it in for the smog test, get the cats good and hot buy doing some spirited driving for about 15 minutes and get it tested immediately. Don't let it sit and cool down.
You need to understand how those "cat ineffectient" codes are set. The normal operation of the UPSTREAM oxygen sensors is that they switch rapidly from .1 to .9 volts. The oxygen sensor generates a slight voltage in the absense of oxygen. When the exhaust pulse is rich in fuel, it will be lacking oxygen, and the oxygen sensor will read .9 volts. When the exhaust pulse is lean in fuel, there is lots of oxygen, and the oxygen sensor will read .1 volts. During the transition, it can read anything in between. The mixture changes in pulses with the opening and closing of the exhaust valves. After the gases pass through the cat, the pulsations will be dampened or moderated. The cat monitor sensors (the ones you replaced and probably ddn't need to) will switch between rich and lean much slower, nearly not at all. When the downstream sensors switch at nearly the same rate as the upstream sensors, it will set the "cat ineffecient" cat codes. The cat monitor that reads the downstream sensors and compares them to the upstream sensors runs ocassionally according to some algorythem built into the PCM. It is the last monitor to run. It will only run after all others have run and you meet certain driteria for how long you have been driving and so on. It can take several weeks or even days for all the monitors to run.
The cat codes tell you NOTHING about the main cat. The downstream sensors are in front of it so it cannot monitor it. If a tech told you that, he is either igorant of how the system works or he is takingt advantage of you.
If the upstream oxygen sensors are getting old and a little lazy, you can have a false reading since the downstream sensors may nearly match the upstream sensors.
You can also have slightly "sleepy" cats simply because they are dirty, and hence the reason for catching up on maintenance including running injector cleaner through the fuel tank.
Some have cheated the system by adding MIL eliminators. Basically they slow down the DOWNSTREAM sensor switching, fooling the PCM into thnking that the cat is effecient. If the car has clean enough exhaust readings (from the precats working at least somewhat and the main cat working fine) you can keep the check engine light off and pass the test. I don't recommend this, but it is part of the knowledge of how the system works.
See, it helps to tell us the problem. I hope you are now better informed.