jdeurisco,
I’m sorry you’re seeing this issue. I have raised a bug for this problem but there are a couple of potential workarounds.
The cleanest one is to use the MyEclipse update site to install MyEclipse on top of a classic/standard eclipse distribution. The instructions can be found on the downloads page.
A rather messier workaround involves modifying the installer. Change to the directory containing the installer and enter (for example):
sed 's/tmp\/oneinstall/home\/tony\/temp/' myeclipse-pro-2013-SR1-offline-installer-linux.run >newInstaller.run
chmod +x newInstaller.run
./newInstaller.run
Note that the new path (in the above example, “home/tony/temp”) needs to be the same length as the path being replaced. The sed command may appear as multiple lines, above; it should be a single line.
Of course, altering the mount to remove the noexec option, temporarily, would also work.
Please let us know if this helps and thanks for pointing out this problem.