The OP's question wasn't actually "Should I save this file where I want to save it?"
The question was "Why can't I?" (Correct?)
Win7 puts a lot of limitations on what you can and can't do. Drove me crazy when I first started using it.
However, I just now tried putting my installation exe file in that folder and didn't have any trouble; got a window telling me I need admin rights and just clicked continue. So you've got something going on with your permissions. (And figuring out the whole "permissions" thing was a freakin' nightmare for me!)
This is how my Win 7 works too. Just tells me I need the Admin rights to do it, but it's just a click to continue. I do have my laptop passworded at boot-up, but I don't know if that makes a difference or not.
That said, I still would never put an installation file in the program's base operating folder. It doesn't belong there and could conceivably cause a problem somewhere down the road which would be a real puzzle to troubleshoot. You just want a clean neutral location for the install file so the if it has to be unzipped, it can extract to the same location, then run the install application .exe file to perform the installation. It can then be deleted or not as the user wishes, because it has no further function in running the program it's updating.