Some apps(Glovebox) apparently need to temporarily stop running when installing new apps. I notice that sometimes when installing an app, Glovebox causes the problem that you are describing, where I can hit cancel but in install button is unresponsive.
They have since fixed the problem, but it still sometimes it takes about 5 secs for Glovebox to pause and make it so the install button is active.
I don't think it has to do with the third party app setting because if you did not have it checked, I believe a pop-up or an error will occur in the installation, but it will attempt to install. It's not like the problem you are describing where it won't even allow you to press the install button.
I'm not sure what other apps have to pause when installing new apps, according to the developers of Glovebox it's some type of security measure, but it's the only app I have that does this.
I'm on an S3 running 4.1.2 so I'm pretty sure it's not a HTC One or Jellybean issue.