Can tablets advertised with Android 4.1, 4.2 or 4.3 be updated? I'm looking to buy an Android tablet, but most give specific versions of Android and of course I want the latest version. It seems odd to me why it matters. Can't I just update the OS to the latest once I get the tablet? The fact that companies always advertise the Android OS version makes me think it can't be updated. Is this the case?
Your tablet will come advertised with the version of Android it carries in the box. When they make it they don't know what versions will be released, obviously. The packaging and advertising will say Ross Tablet comes with Kitkat 4.4. That doesn't mean I won't update my hardware with a newer version of Android, but it means there is no guarantee I ever will.

There's nothing that says explicitely it CAN'T be updated, unless the hardware is insufficient to run a particular build. JellyBean was heavy on resources but KitKat is much lighter. It would depend on this also. 

Either they didn't update their advertising and/or they didn't update the device. There is no hard fast rule. 

Updates to Android itself are creted by Google, then released to the OEM. The actual updates to the device are dealth with by the OEM (manufacturer) and released by them IF they decide they want to. This is after they skin it (Touchwiz, Sense, MotoBlur etc), test it and make whatever changes they decide. This is why I have a HTC on 4.1 and another on 4.4 here. 

Each manufacturer has it's own unique hardware, as does each device model. There is no concept of a 'generic' Android ROM across devices. The hardware and software for it (e.g. the OEM's camera) is closed source and ROM developers have to use their own Kernels and work arounds to get these installed on the various devices. 

You would need to check on a device by device basis. Google should tell you the answer, but XDA Developers is also a great resource.