Responding to your comments.

You stated: "TIGER is from the census bureau, they are as official as it comes." The official record of public rights of way in this section of the road network is the City of Miami Municipal Road Atlas which is maintained by the City's Department of Public Works. 444 SW 2nd Ave, 4th Floor. As an alternative, see here: 
https://miamigis.maps.arcgis.com/apps/webappviewer/index.html?id=b0971e8c87dd4544b5d6fdc180d0a7dd

You stated: "The roads here are way to wide to be service roads." Service roads you identified nearby are the same width. 

You stated: "They are not private as these aren’t driveways or part of a gated community." This is inconsistent with OpenStreetMaps definition. The access = private tag is indicating that the object is not to be used by the public. Further, the Miami-Dade County Property Appraiser's Office shows the roads contained within privately-owned parcels of land and identifies the owner of record. 

You stated: "As for the 'St. Alban's Day Nursery' it is clear that the parking on the side of the road is private from the bing streetside and the property apaisers office but that doesn not aplly to the road in general, drivers backing out of the parking may have priority but that doesn't make it private." I previously provided reference to the private access easement granting this particular business the right to access the private road ("Brooker Street"). The easement can be located online via the website for the Miami-Dade County Recorders' Office.   

You stated: "it can be used by cars passsing through an thus isn't private." There are Private Road No-Thru Traffic signs posted throughout the property. A gate restricts access across across one section. The roads service tenant parking and garbage containers for an apartment complex. Use by cars passing through though possible would be illegal trespassing. 