There is no government or legal definition of "a green company". It's a marketing phrase designed to make people believe that they're giving their money to a business that conducts its operations in as environmentally-intelligent a manner as possible. That isn't always the case.
If a company has recycle bins in its offices, uses soy-based inks, and encourages employees to take alternate transportation - they can call themselves a "green company" but still produce a huge amount of industrial waste and / or carbon dioxide.
"Green web hosting" may be accurate...or it may be another "
bull---t promise". There isn't usually a way for the consumer to confirm or deny a web host's claims of "being green".
Hopefully, solar/wind/water power will continue to develop, mature, and stabilize; and one day we may look on old banners for "green web hosting" the same way we look on some web designer sites of the mid 1990s who advertised "we build your web site, and we'll add links!"