Your statement is true to the original intention of BGS but is factually incorrect given its current implementation. Here are some signs that BGS is a PvP (albeit mediated through PvE) activity, similar to any game of chess or Risk etc:
1. Player minor factions are implemented, which groups attach themselves to and identify with actively promoting. This happened in the backdrop of players adopting non-player factions to promote, which is something that still happens.
2. Missions allow influence rewards to specifically push one faction over another.
3. People researched and calculated relative amounts of activity for indicative influence payout. ie they can and do actively use the delivery of trade goods, bounties, combat bonds, cartographic data, in addition to carrying out signal sources and other actions - with the specific intent and result of promoting or attacking certain factions, to the detriment of other factions, with the knowledge that opposing players are doing similar activity against them.
4. Power play powers get specific benefits and negatives from having certain types of government in control of their exploited systems. Therefore power play groups purposefully effect change on BGS, for their own needs and against those of other power play groups, in addition to this bringing them into conflict with groups that proactively engage in BGS.
Unfortunately for your claim, the idea that the BGS is purely a coincidental background simulation to make the galaxy feel alive and nothing more - has been redundant, irrelevant and inaccurate. Both as a result of player actions, and Frontier implemented mechanics. BGS is very much a battleground for players and player groups to carry out conflicts with one another.