Why does it matter if it's only cards that they actually own?
Proxy-ing happens a lot in casual games IRL.
And on DN, most everyone makes decks that aren't their actual IRL decks.
I have lots of DN decks, and not a one is mine actually.
I have two decks on there that I took my actual decks and spruced them up to how I WOULD make them, however.
Regardless, if dueling on DN, it shouldn't matter if it's actually your deck.
You still built it, and you're dueling with it.
It just means that the cards you can't get/afford that you need are ALSO in reach.
And therefore, in your deck.