I think you fell on the Integrated Tests scam.
Integration tests are about "determining if independently developed units of software work correctly when they are connected to each other".
Legos can be a metaphor for it:
Let's say you want to create a big block, half blue, and half red.
You can make these independent checks if:
The first half is ...
No if it can be done in Unit tests
The answer however is not a yes / no as this is not really a binary choice.
When possible use Unit tests. If you are testing 'based on this information from this interface...", i.e. business logic, then you can mock or stub that interface to provide that specific data for that condition.
In many organizations not all ...