Unfortunately the article is short on details -- I've gotten my Tesla repaired both at independent shops (broken rear triangle glass, which is a tesla part, not a repro), and at Tesla service centers. I've (online) heard horror stories of long parts waits, but it's not clear how or if those waits are different at a Tesla service center vs an indie shop (eg, is Tesla prioritizing their own SCs?). I assume the suit is alleging that independent shops have a harder time sourcing parts than service centers do? If so, it seems like a reasonable case.
Of course, they can't really allege a parts monopoly on its own, any more so than against any other manufacturer, since 99% of the time, repair parts for any car are sourced from the manufacturer via a dealer parts counter. Eventually OE and OEM parts are available through parts stores, but that's an opaque process to the end consumer.
It would also be interesting if the problem here is the lack of a franchise model- in theory I can get my Toyota repaired at one of several dealerships, so technically there's "competition" in the market, even though they all need to hold a franchise to use the name.
And, of course, there would presumably be an outcry if Toyota refused to play nice to indie shops as well.