I remember once having a conversation with the support team of another vendor of third-party backup software, and resigning myself to the fact that I was going to have to use a sysadmin login. No problem - the jobs ran under the SQL Server Agent account, which was sysadmin. The issue you have is that other teams want to take responsibility for your database backups. You should push back on that if you can - you are the DBA and you know best of anybody when, how and how often to back up your databases.

John