If you look carefully enough, you'll find material to read out there which claims almost anything. To determine the risk of 'increased radiation' from a dropped cellphone, one would first have to determine what types and levels of radiation the device created in the first place, and thus whether the casing or normal functioning of the device would actually put the user at risk in normal circumstances, let alone if the device was damaged in some way.
To be honest, I think the notion is nonsensical and likely nothing more than an urban myth. There are devices which can cause harmful radiation and where damage could render the effects somewhat worse than normal - microwave ovens are a good example, where a damaged door or door seal can cause leakage which is not good for humans. Cellphones however are very low power devices, and while there is inevitably some radiation (they are radio frequency transmitters after all) the casing would not be particularly protective - the frequency range is too high. Thus damage caused to the case wouldn't subject the user to any increased risk. Likewise, any internal damage capable of raising the risk to the user would realistically render clear operational issues after the damage was sustained since it would impact on antenna and signal reception.
Since there remains debate about whether cellphones actually pose a genuine health risk at all, all one could reasonably say is that you are not likely to be at any
additional risk unless you also note a degraded performance from the iPhone.
