What does lower interest rates have to do with lower rents?
Taxpayer subsidized interest rates simply transfer future taxpayer money to existing land owners, similar to how taxpayer subsidized educations loans transfer money from future taxpayers to educational institutions and their staff, via excessive tuition prices.
If the government wanted to help someone buy a house, it could do one or more of the following:
1) build more houses
2) pay someone to build more houses
3) give people cash so that they can buy houses.
Houses can be abodes of any kind, including apartment, condo, townhouse, detached house, etc.