They might use the same or similar equipment but they don't use the same operators, wacking some gas in isn't the same as an aircon service.
I think the OP was asking about a recharge and whether any garage could do it, not an "aircon service", or whatever the main dealers sell you.
In my experience, a service consists of a run on the recharge station, and a debug spray or bomb sucked up the vents. The employees at Honda dealers are no more likely to be proficient at performing this type of work than a good independent, and probably far less than a workshop that specialises in aircon systems.
They all use similar fully automated recharge stations, which doesn't just "whack some gas in". It extracts the existing refrigerant and PAG oil, measures the quantities, checks the system for holding vacuum, then refills with the correct amounts of refrigerant and oil. You should receive a printout giving the pre and post recharge figures, and type of gas used.
If you have a vehicle which is 3/4 years old or newer, just be prepared that the R1234YF refrigerant used in newer cars is very expensive, and subsequently the cost of a recharge is also considerably more expensive.
