They're supporting the drivers, not the medallion owners, who are the ones renting the cabs to drivers 6 days a week at an outrageous markup and preventing the city issuing any new medallions. The average taxi driver, who does not own a medallion, gets screwed by the current arrangement and would be far better off working for Uber IMO.

I think they mean "better deal" to be taken ironically by the readers, who likely have little sympathy for cab drivers. Unlike most public unions who are paid by taxes, the electorate is directly and visibly affected by taxi price hikes. So public support for them is naturally much lower than the unions the rich people pay for. Probably anyone reading this is laughing along. They are thinking that fifty cents per thousand feet driven is more than a fair fare (that is the current rate for SF cabs).

Edit: it appears the strike is more about the credit card fees companies charge the cabbies, digital tracking of the cabs, tvs in the back seats which show adverts to passengers, and various other anti-consumer and anti-driver practices. In this case, I can see that public support might be a little higher. I don't like either cabbies or cab companies, but if I had to pick which I like least, it's obviously the companies. In this case, the fair deal bit might be meant unironically.

This strike is not intended to inconvenience the cab customers (voters!).

They intend to prevent vehicular access to City Hall. A few percent of the cabs will be involved in shutting down the streets at City Hall and if Uber takes up enough slack so the customers aren't inconvenienced that could be helping the cab industry. They don't want pissed off voters.

(Personally, it seems ill advised. The core seems to be the cab companies keeping a 5% transaction fee on credit card processing, which isn't far from the cost. Some cabbies also don't want GPS trackers on the company's cars or LCDs playing advertisements to their riders.)