I'm not keen on the conciliatory tone and going straight to a 'bribe' of a refund/offer/etc, but in some markets that could work. If I had it as a response I'd feel like I was getting a brush-off rather than someone was trying to engage with me and fix my problem. If someone is willing to go to the effort of making a complaint without asking for a refund then they're expressing an interest in continuing the relationship; a refund is often seen as "we don't want your custom so we're paying you to go away." Like I said though, it's very dependent on the market.
Generally I think that'd work for the majority of free users of a service. For paying customers, though, you sort of have to triage between minor complaints and ones that will lose you a customer quickly if you don't look like you're solving it.