As part of a reply to another thread on the same topic I found a help topic that referenced YouTube and fair use:

Using materials from EA games

EA appreciates the passion that players have for our games, and we're always excited to see the creativity that comes from our community. EA does not object to fair uses of video footage or screenshots on video sharing sites, including YouTube channels that are commercialized, as long as the footage is a version of the game that we have released to the public.

We do reserve the right to address any inappropriate use of EA content. Additionally, because many EA games include content that is licensed from a third-party company or may otherwise have usage restrictions, paired with the large number of video-related questions we get from the community, we aren’t able to grant specific approvals or respond to all follow-up inquiries.

[Source: help.ea.com]

If there is a 3rd party managing this for EA they might have gotten a bit trigger happy on the claims. I hear that's not unusual, there's a recent example of a 3rd party company the was representing Linus Media Group (YouTube channels like Linus Tech Tips, Techquickie, TechLinked to name a few) who send loads of claims to other channels videos that were clearly covered under fair use. This even included copy claiming video's that were made by other channels within Linus Media Group. Turned out it was just a stupid automated system.