Hello Claire. While your husband's fear of acute metal poisoning is a bit exaggerated, he is actually right about one thing: you shouldn't leave tomato paste in an opened tin can in the fridge.
Tomato paste is very acidic, which causes it to react with the exposed metal of the can once the protective lining is broken. This won't kill you, but it will give the paste a distinct, unpleasant metallic taste. Furthermore, once opened, the food is exposed to oxygen and bacteria, and the open can cannot be properly sealed, leading to rapid drying out and spoilage.
To safely store your leftover tomato paste, I recommend transferring it to a small airtight glass or plastic container. Alternatively, you can spoon small portions onto a parchment-lined tray, freeze them, and then drop the frozen cubes into a freezer bag for future midweek pastas.
Best regards,
Chef