If bread falls after you score it, it's because the bread is overproofed. Basically, the bubbles of carbon dioxide have reached the largest size that the structure of the dough can support and the stress of scoring causes it to collapse. They key is to either score it earlier and let it continue rising a bit, or to score & bake it earlier (this works great if you have a very hot oven and can find a way to get some steam into it).
If your neighbor came over with bread and it flattened in your oven, it's possible that hers also overproofed in the time it took to transport it (or the extra jostling of transportation caused them to fall).
The only way I can see it being your oven is if the temperature is way off. Test it with an oven thermometer. Be sure to test different areas of the oven. Some ovens will indicate that they are fully pre-heated long before they actually are. Use your thermometer to test that too. Be sure that you are putting your loaves in to bake at the proper temperature. Some people use a pizza stone to even out the oven's temperature, on a rack either at the top or bottom of the oven, depending on whether your oven is gas or electric.
The scoring should be very shallow, done with a quick motion and with a very sharp blade. Try using a new razor blade.