Ronda scored three takedowns against Miesha in their first fight (source). The first takedown definitely came from Miesha attempting a takedown. The second takedown is from Miesha standing up and grabbing Ronda. You could argue she was going for a takedown, but Ronda held the clinch and took her down 15 seconds later, so that is kind of an extended counter. The third takedown came from Ronda clinching during a striking exchange.

https://www.youtube.com/watch?v=PDxA9Mo5FEI Takedown 1: 3:52 Takedown 2: 6:20 Takedown 3: 7:08

In the second fight, Ronda scored six takedowns (source).

The first takedown attempt starts at 4:50 in the Rd 1. Starts from Ronda clinching in a striking exchange. Ronda doesn't finish with top control, though, and Miesha escapes.

The first completed at 4:05 in Rd 1. Ronda catches a lowkick and takes her down.

The second at 1:43 in Rd 1 was a counter to a TD.

The third at 1:00 in Rd 1 was a counter to a TD.

The second incomplete takedown happens at 4:53 in Rd 2 was from a clinch from a striking exchange.

The fourth at 4:30 in Rd 2 was a TD counter.

The fifth at 4:04 in Rd 2 as a single leg during a striking exchange.

The sixth at 2:35 in Rd 2 was from a clinch. Miesha threw a knee after an extended clinch period at the cage, which started at 3:30 when Miesha was standing up and Ronda maintained control.

The is arguably 5 of 9 takedowns, with one more at 4:30 in Rd 2 that is clearly a takedown that she didn't followup, that weren't counters to Miesha's takedowns, and 4 indisputable ones. So "Ronda has never taken her down without a takedown being initiated first," is flat out wrong.