Liability for what though Loki? Liverpool FC or its supporters have never been charged with anything - it's the families seeking to press charges against the authorities. I'm not sure how Liverpool offering to pay their legal fees could backfire in any way.
It could be seen by some as some sort of admission if culpability or feeling of guilt.
It also sets a precedent that other will compare other situations to. E.g. What if a fan is attacked by another team's hooligans, are they going to get legal aid from their club?