I think it's pretty likely the Twins didn't make Berrios a market value offer.
For one thing, the "Berrios made it clear he wanted to be a free agent" thing is more urban legend than actual fact. I challenge anyone to find a Berrios quote stating that. There's "we've gotten so close to where every player wants to be" from last summer, but that's a far cry from "I won't sign". And, in fact...he DID sign.
2nd, reporting last summer included quotes about he and his family liking Minneapolis, so I don't think the quotes about Toronto are anything different or any indication he didn't want to be here.
Third, reporting last summer included all kinds of talk about Buxton negotiations, but none about Berrios. In fact, just the opposite...there were, according to this article, no offers made.
https://m.startribune.com/jose-berrios-twins-free-agent-contract-status/600079217/
It's impossible to say with certainty, but given the Twins obvious reluctance to give out lengthy market value pitching contracts, I think the most reasonable reading of tea leaves leads you to conclude the Twins never tried very hard to extend Berrios. And didn't try at all last summer.
And personally, I'm ok with that.