The joint sponsor has to wholly meet the financial requirements. For the I-864, if a family member in the same household as the sponsor signs an I-864A, then the income of that person can be combined with the sponsor.
However, it's hard to say how a CO will treat it for the I-134 since it's only a tool to help them make a decision...there's no matching I-134A. I wish I had more info there, but I can just say they will look at the totality of the circumstances. If they both want to fill out an I-134 just in case, then they can do so. Note that the I-134 is not enforceable anyway (the I-864 for AOS is, and the parents can combine incomes there, as noted above).
Normally the UK isn't too strict on the I-134 from what I've read.
