No, Perry did not say the form had to be accepted via internet. You may have inferred that from context, but it is not what he said. The EO said that APPLICATION for the form had to be made available via the internet. The HPV opt-out would still require taking a notarized copy of the state-proved form to the school.
So it looks the same as the Opt out we have now, not easier or harder. I take it this portion of the order was enacted anyways as we can now request the form via the internet.