There is an increased risk of a fire or even explosion with generic cells made from China and I will explain why. The battery industry technically calls the threat "Thermal Runaway". Sounds catchy hun?
What it means is that the intense temperatures that these things burn at (700-900F) results in all cells catching fire. Explosions are also a threat if heat and pressure builds up rapidly.
The most dangerous issues have occurred in the past when metal filings from the cells casing fell into the li-Ion electrolyte inside the cell. (Think of the Dell/Sony battery recall 2008 ish.. I know these are not generics... I will get to the point quickly)
So why are the cheap generics at a high risk???
After the Dell and Sony recalls the major manufactures improved their manufacturing facilities so that all batteries are manufactured in a "Clean Room" akin to what intel uses when making CPU's. It is very expensive to do this. Many generic cell makers in china have not implemented this nor do they pass UL1642 certification.
In fact, Panasonic back in 2009 and Samsung have recently added technology which significantly improves the safety profile for these two brand. Panasonic calls it HRL technology (Heat Resistant Layer) and SFL for Samsung (Safety Function Layer).
Conclusion: Even if a large number of people successfully use these generic cells, that doesn't mean they are safe given what we know now. To me safe means at a minimum
1.) UL1642 certified cells – If you can’t meet this standard then %100 no reason to buy.
2.) Manufactured in a “Clean Room” - (Samsung/ Panasonic/Sony/LG/Sanyo all do this).
3.) HRL/SFL technology – The A+ for attempting to make the safest cells and creating higher standards . Only Panasonic , and some Samsung use this technology
Here is an example of a laptop battery that I bought for my Dell a few months ago – Uses UL1642 Panasonic cells with HRL technology cost is ~$70 which is still much cheaper then OEM at $135 from Dell. Note: My original Dell battery was rated at 5200mAh and this one is rated @ 5900mAh
… so I considered it an upgrade because of the increase in power capacity and 2-3 year service life.
Also, you said you were eyeing a $16 battery. I would be very weary of the sub $20 battery on Amazon and Ebay. Typically li-ion cell that are new cost between $3-$6 when bought in volume. So realistically anything below $25 is most like used, refurbished, or very old. At $16 bucks I would suspect that the cells are refurbish or very old. If they are, expect 8-12 months of service life tops.
$35-$50 seems the average price for a decent 4400mAh that use li-ion cells from a reputable manufacture. At the $50 - $60 range expect 5200mAh.
Hope this helps