Trusting the manufacturer like Google Play I just purchased a Toshiba Excite 10.  I was surprised when I attempted to update manufacturer-bundled software and found that I couldn't because it wasn't installing through Google Play.

Is there a way to make my tablet understand that an app downloaded or upgraded through my OEM is just as safe as something downloaded through Google?
You should go to Settings -> Security and check the option: Unknown Sources (or something like that). then your tablet would allow you to install apps from everywhere.