I'm not honestly sure how AWS Organizations interacts with the AWS free tier.
Rest assured, though, having lots of AWS accounts (and using AWS Organizations, their service designed to _help_ you use lots of AWS accounts) is _not_ against the terms of service.
Each account within the organization gets the limits of the free tier, just as a single account would. I think the reasoning is that if you're going to go through the hassle of setting up orgs then you're probably an enterprise user slated to take the long haul anyway.
Multi Account is a normal pattern for AWS. They even have tools to handle that better like AWS Control Tower. Someone from AWS we talked to even mentioned it as a perk (to get the free tier on every account).
That person was misinformed or maybe the context was outside the scope of business needs. If you use link accounts within an AWS Organization, one of them becomes the payer account with consolidated billing. There's a shared free tier across all accounts. If you actually spin them up as completely separate accounts and don't link within an org, you do get extra free tiers, but most corporations would rather not have the headache that comes with that.