Those cheapo neon bulb testers are not tremendously reliable. There are a couple of reasons why the HOT-TO-GROUND bulb may light in this situation.
The problem is not in the GFCI but you testing methodology.

Further, a functioning GFCI (use it's test button) will detect any hot or even neutral leakage that do not flow back through the unit.

Especially since another unit behaves more normally, it's entirely possible that you've found a manufacturing defect. I've seen some pretty unsettling stuff involving bare wires and shoddy assembly inside cheap made-in-China surge strips, so something similar wouldn't at all surprise me with a GFI device.

I tested another plug-in 6-outlet device I had around, and it also tested with what appears to be a false ground. I agree with ronnatalie that those cheapo testers are not particularly reliable as I had one that apparently had one bulb that was burned out and was not detecting reverse polarity. Nevertheless I purchased another one that I believe is currently working okay as by testing various outlets and devices I have determined that there are no burned out bulbs. However, I do not agree that the testing methodology can be the whole problem, especially since the probe tester also shows a ground-to-neutral connection. The thing is that the 2 devices that looked as if they have a false ground are recent purchases, where as older devices appear to be okay. I agree with davidr that there is probably a manufacturing issue, and I just do not trust the 2 devices that are showing a neutral-to-ground connection, especially since every other surge strip and power tap I had around the house tested okay. (And I have quite a few of these.) I happened to have one other 6-outlet power tap that did not show a ground-to-neutral connection, so I decided to use it. If I can find the receipts I may try to return the 2 devices I think may be faulty.

In the future I will test every plug-in power device as soon as I buy it and return it if it appears to have a neutral-to-ground connection.

"In the future I will test every plug-in power device as soon as I buy it and return it if it appears to have a neutral-to-ground connection."

You need to adjust your "testing" procedure to use equipment that can actually detect ground-to neutral problems.
An analog volt-ohm meter would be a good starts.

Even digital meters can be fooled by 'phantom' voltage because their input impedance is so high.

There have been changes in GFCI devices that may cause the indications you are seeing.

could you have bx wiring or the ground is just pushed back out the clamp against the back of the box, but there be a bonding problem? ive seen this before.

...

Use a continuity tester, on an UN-powered device.

If there is not continuity between the GROUND and NEUTRAL prongs, then stop with this nonsense.

These testing devices are designed to give a quick read. You should not depend on them to tell the whole story. If the tester is bad, return it.

Use a VOM to test the circuit. First test for voltage from hot to ground, then neutral to ground. You should have voltage from the hot to ground. You should find no voltage between neutral to ground, if you do the receptacle is wired improperly.

Test continuity between ground and neutral, you should find no resistance, if you do, the receptacle is wired improperly. The receptacle simply opens the circuit and provides plugs for you so that you can provide a circuit for your plug in device or appliance.

Neutral and ground are tied together in the panel box. You should find no resistance between them. If the continuity test fails, then the wiring is problematic.

GFCI devices will operate on a circuit that does not have an equipment-grounding conductor. It operates on the principle of measuring current from one side to the other. If the current return is not the same as supplied the device shuts off. It works rapidly and protects against accidental shock, it does not protect the circuit. It protects people from shock.

Here is a link that might be useful: How to Use a Volt Ohm Meter for the DIY

the type of wire would be helpful. Is it bx? is it nm? Is it k&t? When was it done?

Well thank you, steveomc, for confusing things.

WARNING: A CONTINUITY TEST OF A LIVE OUTLET IS A DUMB !@#$ING IDEA. As stated, neutral and ground are tied together at the first panel. You SHOULD measure continuity. HOWEVER, IF THEY ARE NOT - and we MUST accept this possibility since it is what we are presumably testing for - THEN THERE MAY BE VOLTAGE BETWEEN THEM, which, depending on the construction of your meter/tester, WILL result in, at the very least, a blown fuse in the meter. IT IS POSSIBLE THAT THE METER MAY EXPLODE OR CATCH FIRE IN YOUR HAND SO JUST DON'T DO IT.

NOW, as I originally suggested, perform a continuity test OF THE OUTLET-SPLITTING DEVICE YOU ARE QUESTIONING. NOT THE OUTLET IN THE WALL. When the device is unplugged from the wall (which is the ONLY time you should be performing a continuity test of it!), there should NOT be continuity between neutral and ground.

Even if they are tied together, depending on how far away you are from the panel, there may be a enough of a difference in potential to annoy the hell out of something trying to measure resistance.