This pufferfish with it’s 400 Mbp genome laughs at that statement:
Sure, it is logical to to posit that more regulatory programming is required to specify more diverse cellular behavior, and that increased programming would require more storage space.
But notice that merely predicts a requirement in terms of relative size (A requires more than B), it doesn’t predict an absolute value (A requires 3Gbp whereas B only requires 1Gbp) and it completely fails to explain the observed variance within and between different clades.