Depends what you want to achieve. cguy can confirm, but I suspect it's rather unlikely that you'll get very far on coursera courses, when interview at boutique investment firms that run algos and similar. So at some point, you need a more formal qualification.
Nonsense.
Come work in my business, I hate PhDs and we do plenty of ML, Data science, etc.
DISCLAIMER: only scrappy punks who regularly overflow with passion allowed.
It really depends on the level one is working at, and what one is trying to achieve. We've almost never actually hired someone with an "ML" PhD. Most of our ML experts have their PhDs in stats, maths or physics (who now average over a decade of data analysis/science, ML/prediction work at the highest level each), and the emphasis is looking at the data and predictions, and figuring out what factors are preventing optimal prediction, what optimal prediction actually is, how the data should be transformed, how the underlying algorithms should be changed in order to accommodate this, and how this can be done efficiently in a performance competitive live environment, and also how training for our system can be done at scale.
The optimal training is typically going to come from having a very solid mathematical and/or statistical background, and for those implementing the production code, an excellent CS background with low-level performance skills, in conjunction with the theoretical background.
For many, the job involves cleaning data, and using pre-bottled ML algorithms/APIs (TensorFlow, SciKit, Amazon/Microsoft's ML libaries, OpenML, etc.) (e.g., Creeper's post), and although there is debugging required to get it to work, the kind of statistical debugging required to make novel breakthroughs in prediction quality, and the tight run-time and training requirements that require custom algorithms are often not necessary, and don't need the same kind of people.
So basically, like many things in the world, there are those who build the tech, those who use it, and those who use it and can build their own tech as needed. Coursera courses are fine for most users, and someone who runs through all of them and fully understands their content, will probably be way ahead of the hoards of people using ML tech naively, but they're probably not going to figure out what change to a MLNN learning algorithm is going to improve their out of sample prediction for their particular data sets.
Edit: after replying to Creeper's post, one other thing to emphasize is that the type of work done for the first pass (using existing libraries and tweaking parameters), is very different from what one would do if their goal was to continually improve prediction quality and performance thereafter. For some applications, the first pass may be sufficient in which cases the more advanced skill sets aren't really required at all. For competitive ML (e.g., finance), where better prediction is always an edge, it is an absolute necessity.