All because they opened a relay and got curious. The war that started lasted for a century before they uplifted the Krogans. They only got an FTL drive after the Citadel kindly handed them one in the form of the explorer. They did not get a handy prothean outpost to copy tech from. They barely had any understanding of eezo. The only thing they didn't get was combat holograms and that was because the NCR was desperately trying to maintain a monopoly on them. STG could literally pay prospectors to find tech samples for them, and it wouldn't even be illegal. Plus most of that stuff can be found laying around or stored in pre-war depots. Earth itself was politically divided, so some factions sold tech to gain better relations with the Citadel, while groups like the Followers freely volunteered information. Obviously some of that tech is more impressive than others.
The Citadel got access to Fallout's energy weapons, robotics, cold fusion power cells, advanced biomedical tech, gene splicing, optical stealth, cybernetics, ceramics and heat resistant polymers, virtual reality, terraformers, and vending machines a short while after formal diplomatic contact with Earth had been established.
I had a Fallout - Mass Effect fusion fic planned once that would have kicked that stupid cliché in its ass, though nothing every came of it.
