Generally, wild grapes are more suited to growing on the exterior walls of wooden sheds, garden houses, or near fruit trees, where they can climb from branch to branch. You have opted for ‘cultivated’ planting, which has the advantage of allowing you to keep the vine better ‘in shape.’ Yes, even wild grape varieties need some care and pruning in winter if you want lots of juicy berries. If you are offered this vine (Isabella), then definitely go for it! (https://en.wikipedia.org/wiki/Isabella_(grape)) It has all the characteristics of a wild vine and produces a bountiful harvest.
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I think "California wild grape" is just its name. We have muscadines here which are what we consider more of a "wild grape". I think the kind of got are best cultivated on the wire.
If it is Muscat Bleu, then I agree with you wholeheartedly. It definitely needs to be trained on wires and pruned properly.