That path is valid. Also, with string literals in C# you can declare them like this @".\MyPath\Doesn'tNeed\DoubleSlashes\Because\IUsed@\file.txt"
This tutorial will show you how to access a UNC path with credentials (which you probably need) http://www.codeproject.com/Articles/43091/Connect-to-a-UNC-Path-with-Credentials
Keep in mind that just because the user on Machine A has permissions to access files on Machine B doesn't mean they can do so without entering their credentials.