There is nothing wrong with reading things from /proc. In fact, that is where those tools get that information from. There are actually three files with the command name.

/proc/PID/cmdline
/proc/PID/stat
/proc/PID/status

I believe it is usually obtained from stat.

Solution

Use the -b parameter:

  -b            Displays the executable involved in creating each connection or
                listening port. In some cases well-known executables host
                multiple independent components, and in these cases the
                sequence of components involved in creating the connection
                or listening port is displayed. In this case the executable
                name is in [] at the bottom, on top is the component it called,
                and so forth until TCP/IP was reached. Note that this option
                can be time-consuming and will fail unless you have sufficient
                permissions.

Note The netstat -b command will fail unless run from an elevated command prompt.

Workaround

Filter the process list and find the PID you're interested in:

tasklist | findstr /c:"PID"  

Alternate solution

You can use Tcpvcon.exe instead. No admin rights required.

Tcpvcon usage is similar to that of the built-in Windows netstat utility.

Usage: tcpvcon [-a] [-c] [-n] [process name or PID]

 -a Show all endpoints (default is to show established TCP connections).
 -c Print output as CSV.
 -n Don't resolve addresses.