According to several articles (examples: Ars Technica, The Guardian, Bitpanda.com), in 2014 a single mining pool (GHash.io) came close or even exceeded 51% of total mining hashrate. Different sources quote different percentages - ranging from 42 to 55 percent, but it is enough to say that assuming the claim is indeed about 2014, it is correct and one or possibly two pools controlled over 50% of total mining network for a short period.
Regarding the implication of situation being the same today - GHash.io reaching the critical size was a wake-up call for its members, and membership quickly dropped: it lost around 2/3 of its members, and by the end of 2015 was virtually defunct. Since then, judging by statistics published by btc.com, the largest pools struggled to grow over 25% of total hashrate. That said, the claim is again true at the moment - in August 2022, the three largest pools control 24.2% (Foundry USA), 15.2% (AntPool) and 15% (F2Pool), for a total of 54.4% of total network hashrate.
A clarification on how applicable the term "centralization" is to mining pools: in most implementations (and specifically in GHash case) there is a central organisation that runs the server the miners are linking to coordinate their efforts, validate their work and handle payouts. In a way, the hardware owners (pool members) are renting out their hardware to the actual miner (coordinator). Thus, a malicious network admin in theory is capable of using the network as a whole to perform a double-spend attack, which is the main concern voiced whenever Bitcoin network centralisation is mentioned. How real this danger is depends on a specific implementation; but its existence is one of the main incentives behind the development of decentralised peer-to-peer mining pools.
As far as I'm aware, there were none succesful 51% attacks on Bitcoin itself up to this point.
Note that the relevant fragment of the video is not really concerned with internal vulnerabilities of the bitcoin network, but rather with infrastructure surounding it. Centralized exchanges allow for government control over usage of cryptocurrencies, which undermines several selling points for the whole system; for this particular concern the 51% threshhold is irrelevant, and the total number of users bottlenecked by these centralized services is more important. By my estimations, only ~4-5% (and probably less) of bitcoin network users do not use some kind of centralized pool for mining, and 99.9% use exchanges at some point.