Well, based on that formula, one could say that all religious communities follow a 'liturgy,' in that all of them follow some type of structure. After all, the essence of 'liturgical worship' is thus defined in the Encyclopaedia Brittanica (1911):
LITURGY (Low Lat. liturgic; Gr. X€Ztos, public, and gpyov, work; XEcrovpyos, a public servant), in the technical language of the Christian Church, the order for the celebration and administration of the Eucharist. In Eastern Christendom the Greek word Xetrovpyia is used in this sense exclusively. But in English speaking countries the word " liturgy " has come to be used in a more popular sense to denote any or all of the various services of the Church, whether contained in separate volumes or bound up together in the form of a Book of Common Prayer. In this article the liturgy is treated in the former and stricter sense. (For the ancient Athenian Xetrovpyiat, as forms of taxation, see Finance.) In order to understand terms and references it will be convenient to give the tabular form the chief component parts of a liturgy, selecting the Liturgy of Rome as characteristic of Western, and that of Constantinople as characteristic of Eastern, Christendom; at the same time appending an explanation of some of the technical words which must be employed in enumerating those parts.
By this definition, even a 'holy-roller' service can be considered 'liturgical' in that it has a specific order established prior to the service, even if it ends with utter chaos so long as it is intended to do so and someone is in charge of managing the whole thing (a.k.a. an officiant). The only difference it that the 'sacrament' in such an event is usually an ecstatic state rather that the chnage of bread and wine into Body and Blood.
However, I will be obstinant and insist that wearing my father's helmet does not make me a fireman, no matter how truly authentic the helmet is. Just because someone has picked up this or that and added it to whatever else one is doing does not make the rest 'authentic' as well. We Orthodox see this all the time when some group uses vestments and service books purchased off the internet as proof that they are 'authentic.'
There is something more to worship than the acquisition of bits of 'historical elements,' because the elements themselves have no meaning without their context. This is the inherent problem of the 'reconstructionists' in the Orthodox Church, who decided on their own to leap back through the centuries over what we do now. It has not worked, because this stand ignored the work of the Holy Spirit that got us to where we are now for whatever reason.
The liturgical Tradition of the Church is not an invention, nor is it something tampered with on a whim. It is something passed down through the ages and only changes under the guidance of the common mind of the Synods inspired by the Holy Spirit, which is beyond reach of both parishes and even 'demoninations.' Liturgy is inherently mystical in that there is more to it than just a hodge-podge of texts and books. It is the Spirit worshipping and glorifying the Father and Son through us, so that we might do what we cannot do on our own. Worshipping 'in Spirit and in Truth' is not within our fallen-nature abilities. To use those same abilities to assemble a 'service' makes the service worthless when compared to the true liturgical services of the Church.
The tragedy is that we continue to praise people (i.e. "Nice helment, Giryus! I didn't know you were a firefighter!") for doing what is, in fact, counterproductive to their intended goal. If they seek to worship God, then they need to enter into the ancient Tradition of that worship rather than trying to make it up on their own. Some of those who realize the fruitlessness of such pursuits eventually find their way to the Orthodox Church, where they find the 'real thing' as opposed to 'make-it-up-as-you-go-along.'
I recall members of one group that ended up in the Church having their 'service books' supposedly assembled to resemble 'ancient worship.' What was funny was that the book was full of stickers, covering up superceded versions with newer, yet 'more ancient,' versions of service elements. Eventually, they became so confused, it was much easier to coax then in the door and give them the real thing.
My hope is that, perhaps, we can some day appeal to those looking for the Ancient Tradition and coax them to the Father's Table so they can have the real thing they are looking for.