Why does SQL Server Profiler crash when its run against a DB machine from a client machine?
The profiler.exe will run on the local Windows 7 machine, where you have the Management Studio installed. It will connect to remote instance over network to collect the data, but the profiler.exe itself will run locally on your computer. If you want the collection to happen at the same server where the SQL Server is installed, then you need to implement server-side tracing for that.

A good example of how to set it up, can be found here.

Also by starting Profiler the way you described should first prompt for server details (server name, credentials) even if you have server connection open in the Object Explorer. Now I believe it crashed before ever getting there, so the problem is probably not related to connecting to remote server at all. I would recommend re-installing Management Studio to see if it fixes the issue.

Latest stand-alone installers for SSMS can be found from here.