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Not necessarily. I used mollusks because it's a simple and easy case. I can make my point without getting lost in the details. We can ask the same question for animals of increasing complexity. You begin at simple cases, then move on to more difficult cases.
Taxonomic classifications are built out around recognizable similarities in animals biological structures. Setting aside how precisely we understand brain function in non-human species, it takes little effort to see that most vertebrates are structured in a way that heavily overlaps with human biology. They are similar. Why would you assume they aren't?
And if you go from a "philosophical" perspective and ask how we could possibly know what they feel, you may well extend that to humans. How do I know you experience qualia?
You're getting so caught up in precision that you're overlooking obvious similarities. Can't see the forest through the trees. That animal has a nervous system and demonstrates a pain response. How much more detail do you need to be able to understand it feels pain?
For creatures without similar structures, we don't make the same assumptions about pain and suffering. Do carrots feel fear? Do mollusks weep? No one thinks about that. >

Except for the fact that many people claim to empathize with invertebrates or even plants. You clearly understand enough biology to think clearly about this topic. All I'm saying is that everyone else should make an attempt to meet that minimum standard of understanding. >


many people claim to empathize with invertebrates or even plants.

Very few claim to empathize with invertebrates, but crabs and lobsters and other crustaceans have pain responses too, so it's still not an example on your side here. My point was that people see similarity in responses and behavior, and that's made possible by our very real similarities. That Doctor so-and-so knows the science of it all and Dennis your vegan high school classmate does not makes no difference. 
The science explains why we have similarities and why we see and feel similarities that allow us to empathize. But not knowing the science doesn't invalidate the emotional feeling—the right answer is right whether or not you show your work.
As for people who "empathize" with plants, they fall into two categories: [1] People who are personifying plants because it's a useful rhetorical technique, but don't actually believe plants feel complex emotions; and [2] extreme outliers that don't merit serious consideration. If "crazy people believe crazy things" is your best defense here, you've lost focus on the "philosophical" question your post is about. >

We might just have different experiences when it comes to people's claims about the range of their empathy. I know plenty of not-crazy individuals who either claim to or speak as though they understand the feelings of an invertebrate. I might have a sampling bias because I spend a lot of time around animals and teach HS biology. 
I agree that the right answer is right whether or not you show your work, but showing your work is necessary to distinguish between the right answer and an answer that seems right, but isn't. It certainly seems like it'd be painful to be a clam being eaten by an octopus. This might even illicit a little bit of sadness for the clam... But upon further reflection I might realize that clams don't have centralized nervous systems. They don't have families that will mourn their demise. They don't have unfulfilled dreams or projects. I've now shown my work and realized that my previous answer was incorrect. >

Again, you're pushing out to extremes to justify your position, but if you have to run all the way to mollusks, animals without a central nervous system, to stick to your view, it sure seems like you've abandoned it for every animal that does have one.
And for those, there's no need for people to show their work. Because they're right. Someone else can check it for them. Verified. Instinct to empathy validated.