Agreed. I would also add, I don't think frontend vs backend accurately describes how skillsets are clustered anymore -- especially with JavaScript's increasing ubiquity.
I would cluster skillsets into: ops, development, and design.
Ops: making things highly available, logging, performance monitoring, reliability, deployment scripts
Development: Writing code on both frontend and backend.
Design: Visual design and CSS/HTML
Most developers I've interacted with at various companies write both APIs in the backend and user facing UI. In my experience it's becoming increasingly rare that a frontend developer doesn't also write backend code.
They typically aren't very good at making their apps deployable and highly available, and they also aren't very good at making things look good with CSS. Sure they can do it, but it isn't their specialty and it would be quite a learning curve or it just takes them much longer than someone who does just that.
When hiring people, I like to find people who are strong individually in those 3 areas (ops, programming, design). I don't try to find programmers who can do ops or design. I don't worry so much about a frontend engineer being able to do backend work and vice versa, the crossover is generally smooth and interchangeable.
It is generally easy to find ops, and programmers who specialize and are talented. Designers who can do visual design and code it up are a bit rarer, so sometimes it is needed have 1 person do design and another person code it up.
Also, a very senior person is obviously going to be stronger in each of those areas, so full stack is highly correlated with working experience.