The problem with bacteria is two-fold.
Firstly, some bacteria can double their number in as little as 30 minutes. For the sake of argument, let's say the doubling takes an hour or more. If it is a particularly thick chunk of meat, it will take X amount of time fir the cook to consider it fully thawed. For most of that duration, the outer surface will have been above zero degrees and surface bacteria can start multiplying. Biological systems work twice as fast for every 10°C rise in temperature.
Refreezing requires a second thaw session which only doubles the time available for surface bacteria to multiply further. If there are enough, a handful may escape high temperatures and stomach conditions and cause food poisoning.
Secondly, with botulism, the problem is that the botulin toxin is not destroyed by cooking temperatures, even when the bacteria are. So long as the meat has a continuous history of storage at under 5°C (hint: the boot of your car breaches that specification, albeit briefly) then you should be okay.
Thawing in the fridge may take ages but at least it doesn't mean the surface of the meat reaches kitchen temperature.
In summary: a second thaw extends the incubation time for whatever is on it. If you have handled the meat with bare skin, bear this in mind. Left long enough I have seen refridgerated meat develop surface colonies even though the packaging is unbroken, so the bugs get onto the meat at the factory, afaic.