Social Security gets special bonds specifically to avoid the bond market distortions you describe. They have been purchasing these bonds in high volume for decades prior to the financial crisis, and marketable Treasury rates were much higher for most of that time.
In addition, in 2011, SS tax receipts dropped below expenditures for the first time since 1983, so SS stopped purchasing these special bonds in any significant net volume. (The trust fund is still cash flow positive due to interest earned on bonds they already hold.)
As for the Fed's purchasing program, Treasury rates were historically low before Fed started buying. In fact the historically low rates were why they started buying Treasuries in the first place--with interest rates bottomed out, QE was one of the only levers left to them. You've got the cause and effect backwards.
My understanding is that, all other things being equal, when government/government controlled agencies purchase government debt ("cause"), the result ("effect") is lower interest rates. Here it is, directly from the head of the Fed regarding the rationale behind QE2:
"What we're doing is lowering interest rates by buying treasury securities and, by lowering interest rates, we hope to stimulate the economy to grow faster." - Ben Bernake
This is the fundamental idea behind reserve banking -- the central bank controls interest rates by manipulating the money supply via the purchase of government bonds:
"When the Central Bank cuts the target rate, they must simultaneously increase the monetary base by buying government securities. The growth of the monetary base creates a surplus in the banks, the supply of funds overnight increases, the demand falls and the overnight rate falls.
...
By controlling overnight interest rates, the central bank will affect the interest rates with longer maturity." - Essentials of Macroeconomics
Is there anything in the above that you disagree with?
They were already effectively zero because there has been such strong demand for U.S. Treasury bonds from customers both domestic and foreign, which was my point at the beginning.
If Social Security weren't buying government bonds (ok, not technically treasuries), that same debt would be issued as Treasuries or similar. Greater supply of treasuries means higher interest rates.
If the Fed weren't buying treasuries in the open market, demand would decline and the market interest rate would go up. Primary dealer bids are influenced by the market rate for treasuries, so the interest rate on new debt would go up.