When it unveiled iOS 13, Apple opened up the possibility of Siri working with rival music services via new SiriKit updates. If Apple and Spotify can work something out, you'd be able to play Spotify tunes using Siri from an iPhone without the need to open the app. However, Apple Music would still be the default music service for Siri on Apple devices, according to The Information's sources.
As part of its antitrust complaint, Spotify put up a website listing the reasons it feels Apple isn't behaving competitively. Its main gripe is the 15 to 30 percent fee Apple takes on Spotify's subscription service from the App Store. It feels that by acting as a gatekeeper to services like Spotify, while also offering its own app, Apple is competing unfairly.
Spotify originally said that "Apple won't allow us to be on HomePod and they definitely won't let us connect with Siri to play your jams." However, as The Information notes, it changed the wording, which now reads: "Only recently, Apple announced that it will let us connect with Siri to play your jams...but fails to mention our name ('I want to play [X] on Spotify') and your HomePod will default to Apple Music."
Google's Assistant and Amazon Alexa both work with Spotify, but Siri does not. Apple has used that fact to push its own Apple Music service, which has tight integration with Siri, HomePod and Apple TV (As of recent counts, Apple Music has over 60 million paid subscribers, while Spotify has north of 100 million premium users.) In any case, the news -- which should be taken with a grain of salt -- isn't likely to derail Spotify's anti-competition suit in the EU.