I would claim it, and cross that bridge when (if) you come to it.
If your pension was awarded on the basis that you could not, at that time, undertake any sort of work, it seems unlikely things will have improved since, MS being what it is. So you may not be found fit for work, and the issue won't arise.
Technically, though, the lady is right. If your reason for not seeking work is because the terms of your pension impose a bar on it, rather than because your health doesn't permit, that's a private matter between you and the pension people, NOT a relevant factor in determining your entitlement to benefits.
Worst case, if you were found fit for work (I'm not saying you will be), is you might have to choose between benefits and pension. Since pension will almost certainly be better (and subject to fewer onerous conditions, such as interviews or having to actively look for work), sticking with the pension and withdrawing the benefits claim would probably be the lesser of two evils.
But this is only if, and I do mean IF you were found fit for work, and couldn't get it overturned on appeal.
If you're not found fit for work anyway, you may be able to claim both benefits and your pension, without breaching the terms of either. However, for either type of ESA (contributory or income based), your pension income may be taken into account. If your pension is only small, it might not make any difference. But if it's a generous pension, you might not qualify for ESA.