This is an interesting idea and could easily be explained with scientifically-sound methods.
The main thing that creates metal deposits (we speak more of deposits in the minerals industry, as opposed to veins, which are usually a mode of how metals exist within a deposit) is tectonic activity. Every deposit I can think of off the top of my head - and I'm an exploration geologist, so that's a fair few - has some manner of tectonic influence in its creation. Often that is from the opening up of a new basin caused as a by-product of subduction, meaning there is somewhere for seawater to infiltrate the oceanic crust and be heated up by exposure to the mantle. This causes the water to be able to liberate metals out of the crust and bring them up to the seafloor, where the metals precipitate out due to the change in temperature. This is just one example of tectonic activity driving the formation of mineral deposits.
Where a planet does not have tectonic activity, it will often not have an atmosphere or hydrosphere. It is widely theorised that Earth developed an atmosphere (and as the result of this developed a hydrosphere) as the result of outgassing from the early crust caused by volcanism, which is the result of tectonic activity. 208
There are other ways to get an atmosphere though; massive early bombardment from a comet swarm has been theorised as a way to get enough gas and water onto the surface to develop into an atmosphere.
A planet that formed the same way as Earth that happened to have a much lower amount of radioactive material could have easily cooled down a lot quicker; something like 90% of the heat in the core and mantle of the Earth comes from radioactive decay. Random cosmic chance is more than enough explanation for this. And this would have allowed you to have an atmosphere, as the early heat would have been enough to drive tectonic activity, but this would have stopped quickly as the core went cold without radioactive decay to drive it.
Without tectonic activity to drive their formation, mineral deposits would be very restricted. A way you could introduce a very limited amount of metals into your world would be through the bombardment method discussed earlier. Approximately 1.9 billion years ago, a massive rock smashed into the crust in what is now Ontario in Canada, resulting the formation of one of the world's largest nickel deposits. Sudbury represents a fraction of a percentage of the world's mineral resources, so it is by far and away the exception in the formation of metal deposits, so you could use that as a plot point to explain why one civilisation is more powerful than others. 778