I'd say the ep showed that robots DO have free will they just think they don't.
Which is pretty much what the episode implied throughout. This wasn't a story about whether robots have free will, it was a story about how Bender was affected by his
belief that he didn't have free will.
My view on the subject, if I may wax philosophical for a bit, is that free will isn't a yes-or-no question, that there's no such thing as absolute free will or absolute lack of it. There are simply different levels of constraints upon our degrees of freedom, and those constraints change in different contexts. For instance, if I'm in an open field, I have the freedom to choose where I want to move anywhere I want in two dimensions, but very little freedom to choose how I move in the third. However, if I then fall off a cliff, my freedom to choose my direction of motion becomes immensely more constrained. Similarly, a person living as part of a society has more constraints on personal freedom than a person living alone on a desert island, because that person is constrained by the need to consider other people's rights and entitlements. So it's a balance of different freedoms that places some constraints on all of them.
On a psychological or neurological level, our free will is constrained by our personalities, our beliefs, our inhibitions, our hangups. We might theoretically be free to make a choice in either of two ways, but our personalities might make it impossible for us to make one of those choices (for instance, there's no way I'd ever choose to become a beekeeper because I'm phobic about insects). Sometimes our own habits of thought trap us into consistently making a choice the same way over and over (for instance, always sabotaging relationships, always being too afraid to ask out a girl even when she's clearly interested, always choosing to get involved with an abusive man, etc.), and it may take a monumental effort to break those habits and reshape the constraints on our free will.
So it's relative. We have some freedom of choice, but it's within various limits, some external, some internal. Bender has the freedom to choose whether or not he commits a crime, but as a matter of habit and inclination, he's going to choose to commit it, unless some other powerful constraint comes into play to compel him to choose otherwise. For instance, if he has to choose between committing a crime and letting Fry die, he'll probably wrestle with it for a while, but will ultimately have no choice but to save his best friend.
And it's really no different for the rest of us. We call it programming where robots are concerned, but is it really so different from our own personalities, habits, and reflexes? Fry is programmed to be a doofus. Leela is programmed to be aggressive. Hermes is programmed to be a bureaucrat. Our actions and choices are shaped by who we are, by how our innate psychology and lifetime habits dictate our choices. Perhaps it's not so much a question of whether we have free will, but whether we choose to exert it. Most of us never really do, because we just unthinkingly follow our pre-existing inclinations and don't stop to question if there's another way. Exercising free will is about confronting our own "programming" and seeking to rise above it. And that's what Bender was doing here.
And it's so refreshing to have another
Futurama episode that inspires thoughtful discussion like this.