Well, no. Services like JLPCB or AllPCB have a 1.5 day manufacturing time and both feature express shipping via DHL (APCB for free even). There are tons of services like these. Even 4 layer lead-free boards don't break the bank. MOQ is 1-5 on all of these services.

Even here in Germany, where local PCB manufacturing is usually very expensive compared to the options above, services like PCBJoker exist, which are only about 20 to 30 % more expensive.