Having painstakingly gone through the process of writing 35 page Grant Proposals for a hospital and getting funding from the government on all three occasions, I can assure you that the application process was just a formality and legal requirement.
The funding came through because the grantor had a relationship with the department heads that received the funds.
Obviously, you need to meet the required criteria, and a perfectly crafted application is a requirement, but all things being equal it boils down to relationships.
I've also done that several times; it really depends on the funder. In a surprising number of cases, the funder has wound up with a pile of money and not enough contacts with relevant people, so they really do choose people out of the applicant pool. It can also vary by country. In Europe, for example, how much relationships matter seems to vary north-to-south. In southern Europe it is pretty much 100% about relationships.
Perhaps in reaction to what's perceived as southern-European corruption, in Scandinavia there is substantial pressure on funders to make their decisions based on the official application process. There's a worry that "contacts" means your old grad-school buddy, someone you know from a sports club or weekly board-game get-together, etc., as opposed to scientific merit. There's also (what seems to me, as a foreigner) a strong worry that the process shouldn't be perceived as a sham, which means that at least some proportion of the funds have to be doled out according to the official application route, to prove to everyone that the system works like it says it does. In practice that ethos is upheld at some places more than others, of course, but in some circumstances you really can just apply and get money.
The funding came through because the grantor had a relationship with the department heads that received the funds.
Obviously, you need to meet the required criteria, and a perfectly crafted application is a requirement, but all things being equal it boils down to relationships.