A terrain piece is near the board edge but are not touching and the gap is larger than 1/2 width of a model but smaller than the full width, so if it was 2 pieces of terrain, you could squeeze through it. Because of the board edge, can you squeeze past the terrain?
The rule for "squeezing" doesn't really specify what exactly is preventing you to place the unit fully supported, so yeah you could squeeze between a building and board edge
Agreed, the rule is "Any surface they move on must be at least half as wide as their base." So it refers to width of the surface being walked on, regardless of what is making that surface narrow (scenery, cliff, or board edge).
