That's not technically overlapping tiles. The NES wasn't capable of overlapping tiles (moving, yes; overlapping, not that I'm aware of). A tile is an 8x8 pixel graphic. Each tile is arranged in a 32x32 pixel tile square assembly. Each tile square assembly is comprised of a 2x2 attribute table which defines the colors of each 16x16 pixel area of tiles. There are a maximum of 256 tile square assemblies per stage. Each stage is comprised of two persistent CHR offsets (a set of 64 tiles each) which hold shared tiles (such as sky and shadows, as well as doors and spikes) as well as common sprites (like hearts and coin purses); in addition there are two dedicated CHR offsets which hold the tiles "unique" to the current room. These CHR offsets overwrite each other and only two are ever loaded at any one time. This is why when you walk through a door there are occasionally graphical glitches, because the game is drawing the next room using the previous room's CHR offsets. That's actually where stairs come into play. If you want a drastic change in scenery, you use stairs; but the tile square assemblies still don't change. All of stage 1 in CV3 for example, even the cathedral, is defined by a unique set of 255 (actually less than that) tile square assemblies. The game simply reads the tile square assembly value from the ROM, writes it to the RAM temporarily, reads the value of each tile square assembly, then retrieves the list of which tiles comprise that tile square assembly. It then reads the attribute table and draws that tile to the screen with the appropriate colors.
What you're seeing as "overlapping tiles" is just mixed-and-matched tiles in separate tile square assemblies. Open CV3 in reVamp. The designer of that program did a wonderful job making the tile square assembly editor very user-friendly. You will see how Konami made everything that way. Personally, I'm always amazed at how game designers compiled all those tiles. Many of the tiles are vague and abstract outside the tile square assemblies.
Oh, and Konami didn't even always use tile square assemblies. In areas like the intro, the name entry screen, and the password screen, as well as the Prayer scene, the backgrounds were defined tile-by-tile, no tile square assemblies at all. So no, there are no overlapping tiles.
What's even crazier is only the upper-left tile defined by each attribute table actually defines the collision map. This might be what's throwing you off.

A through D corresponds to one tile square assembly. Each label is over a single 8x8 tile. That sole tile defines the solidity of the 16x16 pixel area around it.