In my opinion, Gleeman tends to overstate this a bit.
It's undoubtably true, but I suspect that the 7 pitcher thing would apply to the vast vast majority of MLB teams. So in that way, by continually mentioning it (on the podcast or in print) he's exaggerating it in respect to how it affects the Twins compared to others.
I think the much more interesting data point would be how many starting pitchers get used for more than 2 starts in a given season. Openers throw a little bit of a wrench in how clean that data is, but in my opinion that type of analysis is more meaningful to what we are talking about. There are ALWAYS going to be spot starters coming up from AAA for one reason or another (illness, double headers, etc), but I don't really care about those very much. How many guys are going to be part of your regular rotation over the course of a season? THAT is what I care about. And I suspect the Twins, over the last decade, use an above average number in a given season.