Question
How far away from a building should river birches be planted and why?

Answer
There are a couple of reason not to plant River Birch near buildings. Grows to 40' to 70', 40'-60' spread. (zones 4-9)

The roots system will be about 1 /12 times the spread of the crown, although they are not known as causing problems with foundations they do seek water and if there were a crack in the foundation the roots could be a problem. Also the root system would be limited on the building side that could cause foliage problems.
The spread being 40-60 feet meaning the branched will reach 20-30 feet from the trunk which will rub the building and will need to Deb pruned to keep the limbs off the building.

If you use a dwarf variety the tree will not grow large and you can plant near houses I expect this is what is planted near the homes you have seen. One of these is

Betula nigra 'Little King' (Fox Valley)

This is a dwarf cultivar of the River Birch and relatively new. Only growing to 8'-10' tall and 9-12 foot spread, it is a great tree for those that love river birch, but only have a small area in which to plant. Similar to the species in all other respects. It could be planted within 6-7 feet of the building.