I used to work in insurance and as a result quite often get involved in debates on how insurance companies work. Prior to working in insurance I used to think like the majority - which comes down to making incorrect assumptions. I used to think that it was unfair that if someone put in an insurance claim for several dents around their car that they had to pay an excess for each one. Howe rude! But after working in insurance I now know that an excess applies to each "event", not each claim.
The two biggest tips I can give anyone on determining what they are covered for are:
1/ How many "events/incidents" occurred which resulted in the damage. There could be a flow on of directly related damage from the one incident. Excess is applicable per incident, and the highest excess if straddling two types of coverage with two different excesses.
2/ When considering what cover you have - think back to "the initial cause." For example if your house burst into flames as a result of a lightening strike it is not a fire claim but a lightening claim. This is a easy example, others are not so obvious.
I can only say ...READ YOUR POLICY. And then read it again because you are likely to have misread a word which makes the difference between be covered and not - even I misread coverage sometimes.
As for all the specialty companies offering LL insurance, I have never found them worthwhile as too expensive or doubling up on coverage when used to top up cover. You can't claim for the same coverage twice from each insurer, and if an insurer is aware another policy covers the risk they are likely to ask the other insurer to contribute (at least that is the way it used to be). It is possible you may get better service from the specialty companies - can't comment on that. It is one thing to have the coverage you require, another to get the service you require if making a claim. I revise my insurance coverage each year and have always stayed with a general insurer - change as coverage/price changes.
By LL insurance, I mean all the insurance - building (if not strata), LL contents (carpet, curtains etc), coverage for damage/loss of rent by tenant, liability etc.