We can reproduce this problem on other PCs that have Office 2010 or 2013 installed with either Visio 2010 or 2013. If Visio is not installed on a computer, then of course you can't edit the embedded Visio diagram, and the image doesn't get altered/mangled. As an example, here is part of an embedded Visio object, in Excel or Word, before double clicking it, which opens up the editor.
Here's what it looks like after clicking off it, and out of the editor, in Office 2013. In 2010, the lines don't thicken, but the lines are partially altered.
I noticed that I can get the same effect if I stay within Visio and copy and paste the selection. If Paste Special is chosen, there are options to paste Microsoft Visio Drawing or Viso Drawing Data (or Pictures). Pasting using the Microsoft Visio Drawing results in the same issue whereas pasting Visio Drawing Data doesn't.