Is it safe to reuse a SqlDataRecord?

This approach seems to rely on an implementation detail (that rows are processed individually), but I don't see any documentation which promises this.

Is there some mitigating factor which renders this approach safe?

As user1249190 points out, Reusing SQLDataRecord is explicitly recommended in the remarks section of https://docs.microsoft.com/en-us/dotnet/api/microsoft.sqlserver.server.sqldatarecord#remarks :

This class is used together with SqlPipe to send result sets to the client from managed code stored-procedures. When writing common language runtime (CLR) applications, you should re-use existing SqlDataRecord objects instead of creating new ones every time. Creating many new SqlDataRecord objects could severely deplete memory and adversely affect performance.

Obviously this recommendation does not apply to usage across threads: The documentation also explicitly warns that "Any instance members are not guaranteed to be thread safe."