An anemic model is simply a data container. It doesn't contain behavior. (This might actually be considered a good thing in the functional paradigm.) The opposite of an anemic model is not a model injected full of domain services. You're describing two extremes -- both are bad.
If you have an anemic model, you're not fully embracing what OOP offers. If you start injecting services into those models, you're likely injecting concerns that don't belong there. Either that or your model is more anemic than you think. Why else would you need the service other than it provides something that's required but missing? (Missing might mean anemic.)
Avoiding both "tells" leads to stronger design. Do you have something in a service that a model needs? Maybe it should be moved to the model. If not, maybe you should reconsider your concerns. A model's behavior should work inside the model. It should mainly (if not only) concern itself with members. But remember, there will still be things that work on or with the model. For example, models shouldn't be opening TCP connections or listening for UI events, even if they're somehow involved. That's someone else's responsibility and that someone never belongs inside the model.