Single Responsibility Principle vs Anemic Domain Model anti-pattern
The quote from the SRP paper is very correct; SRP is hard to get right. This one and OCP are the two elements of SOLID that simply must be relaxed to at least some degree in order to actually get a project done. Overzealous application of either will very quickly produce ravioli code.
SRP can indeed be taken to ridiculous lengths, if the "reasons for change" are too specific. Even a POCO/POJO "data bag" can be thought of as violating SRP, if you consider the type of a field changing as a "change". You'd think common sense would tell you that a field's type changing is a necessary allowance for "change", but I've seen domain layers with wrappers for built-in value types; a hell that makes ADM look like Utopia.
It's often good to ground yourself with some realistic goal, based on readability or a desired cohesion level. When you say, "I want this class to do one thing", it should have no more or less than what is necessary to do it. You can maintain at least procedural cohesion with this basic philosophy. "I want this class to maintain all the data for an invoice" will generally allow SOME business logic, even summing subtotals or calculating sales tax, based on the object's responsibility to know how to give you an accurate, internally-consistent value for any field it contains.
I personally do not have a big problem with a "lightweight" domain. Just having the one role of being the "data expert" makes the domain object the keeper of every field/property pertinent to the class, as well as all calculated field logic, any explicit/implicit data type conversions, and possibly the simpler validation rules (i.e. required fields, value limits, things that would break the instance internally if allowed). If a calculation algorithm, perhaps for a weighted or rolling average, is likely to change, encapsulate the algorithm and refer to it in the calculated field (that's just good OCP/PV).
I don't consider such a domain object to be "anemic". My perception of that term is a "data bag", a collection of fields that has no concept whatsoever of the outside world or even the relation between its fields other than that it contains them. I've seen that too, and it's not fun tracking down inconsistencies in object state that the object never knew was a problem. Overzealous SRP will lead to this by stating that a data object is not responsible for any business logic, but common sense would generally intervene first and say that the object, as the data expert, must be responsible for maintaining a consistent internal state.
Again, personal opinion, I prefer the Repository pattern to Active Record. One object, with one responsibility, and very little if anything else in the system above that layer has to know anything about how it works. Active Record requires the domain layer to know at least some specific details about the persistence method or framework (whether that be the names of stored procedures used to read/write each class, framework-specific object references, or attributes decorating the fields with ORM information), and thus injects a second reason to change into every domain class by default.
My $0.02.
Rich Domain Model (RDM) and Single Responsibility Principle (SRP) are not necessarily at odds. RDM is more at odds with a very specialised subclassof SRP - the model advocating "data beans + all business logic in controller classes" (DBABLICC).
If you read Martin's SRP chapter, you'll see his modem example is entirely in the domain layer, but abstracting the DataChannel and Connection concepts as separate classes. He keeps the Modem itself as a wrapper, since that is useful abstraction for client code. It's much more about proper (re)factoring than mere layering. Cohesion and coupling are still the base principles of design.
Finally, three issues:
As Martin notes himself, it's not always easy to see the different 'reasons for change'. The very concepts of YAGNI, Agile, etc. discourage the anticipation of future reasons for change, so we shouldn't invent ones where they aren't immediately obvious. I see 'premature, anticipated reasons for change' as a real risk in applying SRP and should be managed by the developer.
Further to the previous, even correct (but unnecessary anal) application of SRP may result in unwanted complexity. Always think about the next poor sod who has to maintain your class: will the diligent abstraction of trivial behaviour into its own interfaces, base classes and one-line implementations really aid his understanding of what should simply have been a single class?
Software design is often about getting the best compromise between competing forces. For example, a layered architecture is mostly a good application of SRP, but what about the fact that, for example, the change of a property of a business class from, say, a boolean to an enum has a ripple effect across all the layers - from db through domain, facades, web service, to GUI? Does this point to bad design? Not necessarily: it points to the fact that your design favours one aspect of change to another.
I'd have to say "yes", but you have to do your SRP properly. If the same operation applies to only one class, it belongs in that class, wouldn't you say? How about if the same operation applies to multiple classes? In that case, if you want to follow the OO model of combining data and behavior, you'd put the operation into a base class, no?
I suspect that from your description, you're ending up with classes which are basically bags of operations, so you've essentially recreated the C-style of coding: structs and modules.
From the linked SRP paper: "The SRP is one of the simplest of the principle, and one of the hardest to get right."