I was, I need hardly tell you fellas, much distressed at having gotten this wrong, according to Tim, a native speaker and stalwart Man of Kent who ought to know about such things. I have at one time or another taken some pains to inform myself about all manner of niceties of the Queen's English, and I could scarcely believe I had been so self-deluded.
But I was not, and I have the incontrovertible proof in hand: if you have half a minute to spare, boys, kindly direct your attention to the following marks in these episodes of the endlessly fascinating BBC art-investigation series Fake or Fortune? - one of the regulars of which is the eminent art historian Bendor Grosvenor (B.A., Camb.; Ph.D., E. Ang.) - a scion of the Dukes of Westminster, as anyone could guess by his heraldic name alone - whom I reckon no one could accuse of having an incorrect, or even an inelegant vocabulary.
Please listen for just a moment to him saying "I reckon" at about the 5:15 mark of this 2014 episode on a work by Gainsborough, and again at 5:30:
And likewise at about the 25:15 mark of this 2012 episode on a work by Van Dyck.
Presenter Fiona Bruce says it at about 2:00 in this episode on a work by Winslow Homer:
And ceramics expert David Battle uses the verb in the interrogative at about 3:45 in this clip from Antiques Roadshow:
I. Rest. My. Case.