Sorry but that's misleading rubbish.
If you have 3rd party indemnity that covers you against a 3rd party claim, providing you're acting legally.
You appear to be commenting on making some sort of legal claim yourself against someone else, which is nothing to do with you having 3rd party cover, indeed if anything that would be the legal expenses bit they have dropped.
Depending on what your claim was it might be one for a "no win-no fee" set up, or it might be one for your solicitor to look at.