Is there such thing as Fake power?

It's not "fake" power, but some third party charging docks, as well as a lot of non-Apple PCs don't provide enough CURRENT to charge a battery properly. They may meet the USB power specs for voltage, but don't have enough umph behind the volts.

Another issue is the device which provides too much voltage... there was at least one third-party speaker set which would actually burnout iPhones. We found out the hard way at the store, when customers began popping their iphones in to test the speakers out, only to have their iphone "popped" instead.

Try charging your iPhone using the wall charger and cable it originally came with. go straight into the wall, don't use a power strip, etc... Try this for several charge cycles (a week or so) and see if the battery life improves.

Some usb docks on keyboards don't supply enough power to charge an Iphone so I suppose your Ihome could be doing the same thing. Use the wall adapter or a usb on a laptop or pc and see if it charges regularly.

I personally saw my iPhone give a warning stating "only 20% power remaining" and the iPhone was fully charged using the iPhone wall (a/c) charger--a few moments later the iPhone showed a 99% charge. I'm pretty sure there's a bug in need of fixing in the iPhone OS. 3rd party chargers or not--Apple's got a problem, not 3rd P charging systems, IMHO.

The 99% charge is nothing, happens on laptops as well, it has to do with battery health and a variety of factors that are used into calculating battery percentage.

What they most likely meant, is a fake AC Adapter, that thing you plug into the wall.

I've used cheap chinese ones before, and the screen would become less accurate. It has to do with the amount of noise emitting from the charger. Let me tell you, anything that is suppose to be emiting a DC current and is emitting some AC, voltage spikes and the such, with it which isn't something you want to deal with in your circuits.

I got a refund for the AC adapter and got a OEM apple charger, and like magic my screen works perfectly while its being charged.

Also, the iPhone is rated to handle up to 1 Amp at 5 Volts, most chargers such as standard usb charger uses 500 milliamps(mA) which is completely fine (just takes longer to charge). Usb chargers are also in a computer that generally speaking has a well built power supply that provides a very steady DC current.

Having less current is fine, it charges slower, having to little voltage causes irregularities and having spikes or two much of either current or voltage will burn out an electrical device generally.

That chinese 1-3 dollar iPhone adapter on the other hand, will not. Not all AC usb adapters are built the same, believe me I burnt out an old windows mobile phone back in the day to prove it.