The complaint correctly says that the Obama Administration has been assuring Congress and the public that the nuclear inspections can be used to obtain intelligence on Iran's nuclear facilities which will assist us if we have to go to war in the long run.
The Iranian complaint also correctly points out that the agreement bars the US from using the IAEA for intelligence gathering purposes.
This effectively cuts off the Obama Administration from discussing the agreement at all, since their main talking point is now considered in breach of the agreement itself.
The agreement specifies that any of the parties can treat “significant nonperformance” of the agreement “as grounds to cease performing its commitments under this JCPOA.” If Congress rejects the agreement at the end of their 60 day review process, Iran can justify backing out of the deal as well, but now due to the complaint against the US being true, the UN would reject a war with Iran over them reneging on the agreement (which is also what the Obama Administration has been promising would happen if Iran backed out).