I think it's just because there's a general consensus that it's better for babies skin to use non bio and that biological detergents are more likely to cause irritation.
I don't think the washing label is suggesting that using bio would cause damage to the nappy itself.
There's a sticky on the "washing nappies" board which goes into detail about all the issues with bio/non bio detergents - it would seem that actually there's very little evidence that bio does cause skin irritation, and the numbers likely to be affected by any irritation are seriously small.
Loads of the mums here use bio with no problems. I've also recently switched to bio (I use BGs too) - I find it cleans much better and to my surprise (as I'd always though bio caused irritation), my baby's and my own skin has been fine!