Yeah I saw they said 'seven or more. I don't know about all-time/every year, but crudely, this isn't too hard to figure out.
In 1993, before realignment and the WC, all teams played each other 12 or 13 times, across both divisions. Seems safe to say those numbers would been the same or higher for all of baseball history, given there were also fewer teams.
In 1994, the Phillies did in fact play two teams seven times, and three teams six times. In '95 they had just one seven-game series and no six-game series. Neither of those things in '96, or the first two years of interleague play. After Arizona and Tampa joined it became more common, and continued to be with the 2012 wild card addition. 2013 is when the schedule officially became 19 division games and either six or seven against the other NL teams, which has continued (with some variation in frequency, even as they also reduced division games and expanded interleague) since then.
So this is likely a "record" solely for the post-1993 era. Which is still a lot of fans' lifetimes at this point!