No. The standard spelling is Dia duit, because words are only lenited when there's a reason to lenite them and there is no source of lenition in that phrase. It's a different story in some of the dialects, where Munster lenites duit after a word ending in a vowel, in Connacht it's always dhuit and never duit. So you may see people write Dia dhuit but they are using a dialect form, not standard Irish.
Like all such common phrases that are uttered dozens of times a day, the actual pronunciation doesn't always reflect the spelling, and most people learn this time of initial phrase aurally long before they understand the rules of spelling and pronunciation, so many people first encounter this phrase in the spoken form that you hear here, even though it doesn't conform to the standard spelling. Like "hello", "hallo" and "hullo" in English, it's not something that people worry to much about - I know what people mean when I hear the greeting, and it doesn't matter whether the pronunciation exactly matches the standard spelling.
This is a recording of a native speaker saying dia duit - there's nothing wrong with it. Other speakers would have a slightly different pronunciation, in much the same way that "how are you?" mutates to "how'r ya" and "hiya" and "hi" in English, so if you find another recording that sounds different, it's not necessarily a case of one being right and the other being wrong - they may both be right.
As SatharnPHL said that is the correct pronunciation.
I think every native speaker pronounces it with a H, Dia Dhuit. But the Standard Written Irish is Dia Duit. It’s more important to get the pronunciation correct. You will find a lot of instances where Standard written Irish differs from spoken Irish.
You'll find lots of instances where one dialect has a strikingly different pronunciation of a particular word, but the "standard" spelling usually reflects one of the dialects.
I say "standard" spelling, rather than Standard spelling because it is more of a de facto standard than an official standard - An Caighdeán Oifigiúil only addresses grammar, but even people who quibble about standardized grammar accept the utility of standard spelling.