They symptoms of "regular" covid and the delta variant are not different from each other. That is a ridiculous claim on your part. The delta variant is considered likely to result in more severe symptoms, but that alone is not an identifier.
And he's not saying there are no labs that can tell the difference. But, your typical hospital does not have a lab that can do gene sequencing, as the equipment is expensive and there are few reasons a hospital would even find that ability beneficial.
Hospital may send samples out for testing to determine which variant it is. But they are not going to be able to send samples out for every case they come across, and it impractical to do so.
The numbers we have assume that the samples sent out are representative, and extrapolate that percentage onto the number of cases as a whole. However, the numbers are most likely not representative, as doctors are likely to make judgement calls about which patients samples they send for gene sequence testing.
Caption this Meme 
