Can anyone help me with a curly grammar question??

My children's school has recently adopted the motto "To learn is living fully." I have approached them saying that this doesn't sound right to me - that surely "To learn is to live fully" would be more grammatically correct. But they didn't agree - they think it sounds fine! So now I am trying to find out whether there is indeed some grammatical rule that is being violated by this strange construction that they have come up with.

I have poured over grammar & usage textbooks, learning more than I ever knew before about copulative verbs, gerunds, infinitives etc, but none of them has dealt with this specific issue of whether it's OK to have an infinitive and a gerund on either side of a copulative verb. Or have I misunderstood the structure of this sentence??

Any grammarians out there who can help me with this one? Or if this isn't the right forum for this question, can you point me to someone/somewhere else I could ask it??

Thanks!
Kate