Yes I absolutely think it's highly likely you are giving that impression. I expect they are saying to each other 'don't worry, if she thought she had a decent case to bring she would be bringing it.'
It doesn't matter whether you said wouldn't or couldn't, the impression you are giving is that you are not prepared to meet with them unless and until they've offered you something, meaning you've effectively asked for money twice in two days.
Broadly speaking these things usually go three ways. Employees who know they have a really good case and plan to go to tribunal do exactly that. They complete the appeal process then immediately issue an ET1 claim form.
Employees who feel they have a decent case but for whatever reason (stress, cost, risk of failure) would really rather not bring it unless absolutely necessary get a solicitor to write on their behalf setting out exactly what claim they have, possibly setting out the amount of compensation they would expect to get at a tribunal, fully costed, and saying that in the absence of a favourable response by x date a claim will be filed.
And there's the third set of employees, who feel aggrieved at their treatment, don't think they have a good or worthwhile case, but think it's worth chucking in a stroppy letter in the hope that they'll have some 'stop hassling us' cash shoved at them. Employers really don't like people who do that and are not particularly worried about them.
I expect they are viewing you in the third category and you can imagine which of the three categories is most likely to get a decent offer to settle.
If you are genuine about wanting to take them to a tribunal you need to put yourself back in one of the first two groups. I'm assuming as you haven't said yes, that you haven't yet got your solicitor to write formally as I've described, and have instead written yourself. I would suggest you either get your solicitor to write along those lines, or bypass that and issue an ET1 claim form. By doing either of those things you are more likely to get yourself taken seriously.