Things which could be at the root of this misunderstanding include:
* The fact that we operate a *strictly optional* logically centralised directory service to look up matrix IDs by email address or phone number. I really wish we'd never added this to Matrix; it causes way more grief than it solves - we'd have been better off waiting off for someone to build a decentralised keybase service and use that instead.
* Element runs a centralised integration manager (aka app store) to make it easier to add bots/bridges/widgets to rooms. Again, this is completely optional - although back in 2019 we had a stupid bug in Element Web which meant it checked the integration manager even if you weren't using it. This was fixed in June 2019 (https://github.com/vector-im/element-web/issues/6802).
* Element has to query your server to find out what authentication mechanisms are available before you log in. Therefore if its config points to the default matrix.org homeserver, you end up pinging that every time you log in, even if your homeserver is elsewhere. The solution for now is to change your default homeserver in the config to avoid this.
* Servers need to be able to validate events from servers even if those servers are offline. To do this you need to grab the public key for the offline server from somewhere; by default Synapse uses matrix.org as a fallback, but loudly nags the admin to pick a better default when you install the server.
None of these actually allow a "central authority to have influence on another server" though; I've just listed the only places I can think of where a typical self-hosted Matrix implementation might interact with centralised services run by Matrix.org or Element.
Unfortunately I think the real root of the misinformation is that it's just a bit too tempting and easy to throw around FUD. Some day we may get to the point where alternative FOSS projects will realise that the real enemy are centralised proprietary user-exploiting services rather than one another...