You don't know if it was a lie about the club being opposed to the £30 away cap or not, you're presuming it was a lie.
As far as I recall, as it became clearer, there wasn't a vote on whether or not a cap should be imposed, but a canvassing of opinions of all Premier League clubs from the PL big wigs. In which meetings, we apparently made it clear we were opposed to it, along with several other clubs.
You're presuming it's a lie in the same way others are presuming it's true.
There is evidence it was true given the club's that were in support of it were beginning to discuss mutual agreements of caps for away fans at their respective grounds, once those league wide cap discussions hit the buffers due to other PL clubs opposition.
We were not one of those clubs discussing mutual agreements.
Then the protests at Anfield happened, gained a national audience, and that tipped the scales with the £30 PL wide away cap following not long after.
So unless you have anything that points to it being untrue that we were opposed to the cap, then it's quite clear you're guilty of presuming also.
As an aside, re your final point, that's a pathetic argument for not protesting. Those who chose to protest would be doing so for the benefit of those who chose not to take part also. Anyone looking at this from such a perspective would be guilty of being extremely short sighted, and not looking at the bigger picture.