https://en.wikipedia.org/wiki/FCC_Open_Internet_Order_2010
The key about the 2010 rules is that they did not reclassify ISPs. These rules were similar (actually much weaker) to the 2015 rules, but they were issued under the authority the FCC claimed to have over Title I services. As most here know, from 2005(ish?)-2015, cable/fiber ISPs were regulated under Title I.
ISPs sued and argued that since they were Title I services, the FCC's 2010 regulations were illegal. The judicial system agreed (Verizon v. FCC 2014). The solution to this problem -- the court explicitly told them this -- was to reclassify ISPs as Title II services; FCC would then have the proper legal authority to re-issue their NN regulations. Wheeler's FCC did this in 2015.
This is wrong, but oddly not quite as wrong as the FCC chair’s description as it at least as some connection with reality.
Enforcement of “net neutrality” rules (the FCC name was always “open internet”) has gone on for quite a long time, first under a casd-by-case regime without specific regulations and from 2010 under Title I regulations that were substantively similar to the Title II regulations adopted in 2015 (though they had looser rules for mobile broadband providers.)
The court struck down the case by case approach in 2010, and the Title I approach in (IIRC) 2014, specifically pointing to Title II as the authority that the FCC needed to invoke if it was going to apply rules of the type it adopted in its Title I regs in 2010. So, in 2015, the FCC turned around and adopted rules under Title II.