The prophet PBUH said:
قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ : ( إِذَا سَمِعَ أَحَدُكُمْ النِّدَاءَ وَالإِنَاءُ عَلَى يَدِهِ فَلا يَضَعْهُ حَتَّى يَقْضِيَ حَاجَتَهُ مِنْهُ ) رواه أحمد (10251) وأبو داود (2350) وصححه الألباني في صحيح أبي داود
If someone hears the Athan and in there is a plate in his hand, do not leave the plate until you are done with it.
There are 2 views to this hadith. Many scholars went with the reasoning that Bilal used to make Athan before the Fajir time and then again After Fajir time, according to the following hadith:
( إِنَّ بِلالا يُؤَذِّنُ بِلَيْلٍ ، فَكُلُوا وَاشْرَبُوا حَتَّى يُؤَذِّنَ ابْنُ أُمِّ مَكْتُومٍ ) رواه البخاري ومسلم
Bilal used to make athan at night, eat and drink until son of Um Maktoom makes athan.
The Majority of scholars went with the timing according to the Quranic Ayah and that if you know the Athan happens after that you have to stop if before you can continue to finish. Umar ben Alkahtab used to say:
أن عمر بن الخطاب كان يقول : إذا شك الرجلان في الفجر فليأكلا حتى يستيقنا
If two people are in doubt if the Fajir time came or not, they should eat until they are certain of the time.
Here is the source + full explanation in Arabic if you want:
http://islamqa.info/ar/66202