When I suggested knit_root_dir and intermediates_dir arguments of render in my previous post (now deleted), I actually meant to specifically supply the path to the directory where the user have write access like this:
rmarkdown::render(input = "<absolute_or_replative_path_of_the_Rmd_file>",
output_dir = "<absolute_or_replative_path_of_the_directory_where_final_results_are_desired>",
knit_root_dir = "<absolute_or_replative_path_of_the_directory_what_will_be_working_directory_during_rendering>")