Sounds like garbage to me. They dont "NEED" to go through your neighbors garage. Thats just someone being lazy and not setting up a DEDICATED line for you. I'd ask questions immediately and demand answers. If your paying for a service your not getting, ask for a refund, give it 30 days TOPS, if it takes longer go to the BBB and file a complaint, get your money back and move to a different service. Im already looking into getting comcast fiberoptics or "infinity" to replace verizon if my speeds keep just magically disappearing.
As for your issue. Its not hard to make the fiber optic ends, or what not, just the tools to make the plugs and or parts are expensive thats all. I contract out for that sorta thing so i dont see the problem with why their giving you the run around.
Keep a log of all activity, ticket #s, any form of logging, and if your allowed to within your state, notify them you'll also be recording the call when and if you do make any calls with verizon customer support so that you have proof of your attempts to get help for a service you pay for but haven't been getting. This just strengthens your resolve to get a refund, and or basically lash out and give you a good reason to move over to a provider who does care.
Personally i'd wait though, try exausting your resources, go into a verizon store directly and ask questions, ask for the name of the person, and keep that information logged. Make sure you get valid contact numbers of who to talk to, and who will give you a check up with. If their not holding their end of the contract, providing you with a service within a reasonable time, then you can easily get out of a contract with verizon. Just a heads up.
Edit: Also engineering is just another fancy name for a technican they send out to the work site (in this case your house) to basically run a direct FiOS line to your house (dedicated) and or get out their to do what they gotta do. Most likely its FiOS cabling, and then the making of or salvaging of a coax to link your box to whatever your going for.