Face it, modern fiat money is NOT backed up by anything. Backup up means: you can go to the bank and get your backup in place. You cannot go to the FED and get stuff for your money. So no, it is NOT backed up by the assets the FED bought.
The reason why the FED buys stuff to issue money, is not to have those assets as "backing" (which would mean you could get those assets against any amount of money if you wanted to) ; but rather to avoid the blunt visible seigniorage to be too evident. The trick of buying up stuff against freshly printed money instead of just issuing it makes it look like "a fair deal" and a bit less like a "counterfeiter", and in fact, its economic effects are also less severe by doing so: the seigniorage is more indirectly distributed instead of being concentrated to those receiving the freshly printed bills without counter value.
If the FED were to print truckloads of bills and just send them off by mail to "their friends", it would be too obvious.
Now, "their friends" have to exchange stuff against bills, so it looks like it's a fair deal. And in reality, it is somewhat fairer too.
But the stuff that is bought is no "backing" for the money printed. It is not like as if it were backed by, say, gold, so that you can redeem your bills when you want against gold.
A mortgage is backed by the house you've bought with it, because the bank can come and take your house if you don't pay your mortgage. But that's not possible with the stuff the FED has bought up.