I was told by my broker that the amount of money I invest would be spread across multiple banks (which are FDIC insured) so that at each bank the amount would not exceed $250K. Is this how CDs offered by brokerage houses (that are not themselves FDIC insured) offer protection?
I would say "yes" to your question. CD's purchased from a bank on your behalf by your broker will be FDIC insured and safe. However, be aware that no one is examining the broker except you to ensure that each CD is actually purchased from an FDIC insured bank. Don't trust them blindly.
Remember, the broker should not originate the CD, so the broker's lack of FDIC protection is irrelevant. The job of a broker is to buy things on your behalf. If your broker does that appropriately and sticks with FDIC insured CD's, you will be insured.
Given the risks and gotchas mentioned in the link, buying directly from a bank instead of through your broker still sounds like good advice to me but you can make your own decision based on your level of trust and aversion to inconvenience.
If you buy a CD through a brokerage, the trade confirmation will indicate whether the CDs is FDIC insured. Unless you have authorized the broker (in writing) to exercise discretion in your account, meaning they can act in your account without contacting you first, they must contact you and discuss the specific investment with you before buying it. If they have misled you and the CD is not actually FDIC insured, you have a right to ask them to reverse the transaction.
Keep in mind that brokerages are also required to insure the assets in your account which they hold on their balance sheets (cash, bonds, stocks, mutual funds, but not commodities). This is provided by SIPC, the equivalent of FDIC in the brokerage world. Most large brokerages also insure you beyond the SIPC minimum. Keep in mind, unlike FDIC, you're not insured against market risk, only against a bankruptcy of the brokerage. Also, SIPC is funded by the securities industry, not by the US Government.
I was told by my broker that the amount of money I invest would be spread across multiple banks (which are FDIC insured) so that at each bank the amount would not exceed $250K.
Has nothing to do with this:
Is this how CDs offered by brokerage houses (that are not themselves FDIC insured) offer protection?
If you want a CD, get the CD from a bank itself.
The broker may be purchasing the CDs through a CDARS participant financial institution. You can bypass your broker and go to a CDARS participant FI yourself. CDARS is a network of financial institutions that spread your deposit across multiple FIs, guaranteeing your FDIC coverage. The advantage is you have a single point of contact - your chosen financial institution. You do not have to have any contact with the other FIs where your deposit may be spread.
In fact, on your statements or online banking it will appear as if your large CD is all with your chosen FI. The spreading will happen behind the scenes. A local participating institution can help explain this program to you.