Connection Xbox live with EA Access

EA access discounts are offered by the publisher and are not connected with Xbox live gold discounts. As I see it the main attraction of EA access are the Vault games so its your choice really if you want to use it.

It sounds like your EA Account is linked to a different Gamertag. You can manage this connection over at
http://ea.com, or if you need assistance you can get that from
http://help.ea.com/.

Here is a snippet from the EA Terms of Service: (I highlighted the portion you need to pay attention to)

*

The Xbox LIVE® Terms of Use

The Xbox LIVE® Terms of Use continue to apply in their entirety and govern your conduct while accessing EA Services through Xbox LIVE®. To the extent that Xbox LIVE® Terms of Use conflict with the EA Terms of Service, the Xbox LIVE® Terms of Use control.
EA is solely responsible for the operation and content of EA Services. Microsoft may collect and use information about you and your use of Xbox LIVE® while accessing EA Services through Xbox LIVE®. Microsoft's use and collection of such information is governed
by the Xbox LIVE® Privacy Statement (available at xbox.com or by calling 1-800-4MY-XBOX).
BY ACCESSING EA SERVICES THROUGH XBOX LIVE® YOU HEREBY AGREE THAT MICROSOFT SHALL NOT BE LIABLE FOR ANY DAMAGES OF ANY KIND THAT YOU MAY SUFFER WHILE ACCESSING EA SERVICES THROUGH THE XBOX LIVE® SERVICE, AND YOU HEREBY
WAIVE ANY AND ALL CAUSES OF ACTION AND CLAIMS THAT YOU MIGHT BE ABLE TO ASSERT AGAINST MICROSOFT ARISING OUT SUCH DAMAGES OR YOUR USE OF EA SERVICES. EA is solely responsible for providing all customer support and billing for services obtained through
EA Services.

Those games are from EA vault.

Do you have a subscription to EA access or a trial promotion for it from the new xbox?

http://www.xbox.com/en-GB/entertainment/xbox-one/live-apps/ea-access

Conditions, limitations and exclusions apply. Excludes Titanfall 2. See ea.com/eaaccess/terms and ea.com/eaaccess for details. Availability of play first and vault titles may be limited by territory. Xbox Live membership, acceptance of Microsoft terms
of use https://www.xbox.com/legal/livetou and EA Access terms http://www.ea.com/eaaccess/terms, internet connection and EA account required to subscribe; Xbox Live Gold membership required to access certain vault and play first title online features. Must
be 13+ or the minimum age designated for your territory to create an EA account. EA privacy and cookie policy and user agreement available at www.ea.com. EA may retire this service and/or online services associated with vault titles after 30 days’ notice posted
on www.ea.com/1/service-updates. Available on the Microsoft store and on xbox.com. Titles require acceptance of product end user license agreement (EULA) to play. Internet connection, EA account and acceptance of EA privacy and cookie policy and user agreement
required to access online features. EULAs and additional disclosures available at www.ea.com/legal. After your Xbox Live Gold member trial or EA Access subscription ends, you will not have further access to membership benefits, including vault titles, game
upgrades, or in-game purchases made in a vault title unless you separately have access to that vault title.

"these are the conditions that are in the xbox site about the game"

https://www.xbox.com/en-US/games/battlefield-1