This claim is rubbished by the example of Mufti Taqi 'Usmani mentioned earlier. Can these 'Ulama claim to say that they are busier then Mufti Taqi 'Usmani?
The purpose here is to highlight that many 'Ulamah in general do not reply or even care to acknowledge a question. The fact that they are very busy and do not have time is baseless.