I believe it is true, and she said it was her money that was taken from her by force, which is correct.

In my opinion, if your property is stolen from you, then meted back in dribs and drabs, it is not an entitlement. It was yours to start with.

The one that gets me is that "she died penniless, and alone"... Um. NOT penniless for crying out loud or Peikoff would have had nothing to inherit. And the alone bit. Even if she did die alone, it would have been because SHE WANTED TO. Why is choosing to be alone always demonized anyway? Some people prefer it. These critics are really great at grasping at straws.

“Since there is no such thing as the right of some men to vote away the rights of others, and no such thing as the right of the government to seize the property of some men for the unearned benefit of others—the advocates and supporters of the welfare state are morally guilty of robbing their opponents, and the fact that the robbery is legalized makes it morally worse, not better. The victims do not have to add self-inflicted martyrdom to the injury done to them by others; they do not have to let the looters profit doubly, by letting them distribute the money exclusively to the parasites who clamored for it. Whenever the welfare-state laws offer them some small restitution, the victims should take it . . . .”

– Ayn Rand, from The Objectivist, June 1966, 11 (Via the Ayn Rand Lexicon).

"The last posting claimed that Rand subscribed to Medicare and Social Security at the end of her life and asked her actions undermined her philosophy. "
Did it undermine her philosophy to pay legally-required taxes to those institutions? I say no. So it's not immoral to take benefits she's legally entitled to.

Suppose someone opposes taxes to fund roads and calls for a system of private fees that float with supply and demand (i.e. more expensive at rush hour). Would we condemn that person for using the roads and paying taxes as they are today?

It's like they're scraping the bottom of the barrel for something to criticize her for.

No, it didn't detract from her philosophy at all. Taking a little bit of your wealth back that was forcibly taken from you during your productive years is no sin against objectivism.

In a way, it can be seen as a moral imperative to take as much as possible as a method to over-stress the socialist system that stole from you in the first place. She certainly didn't give up producing while she was physically capable of doing so and become a 'moocher' on the system. She only used a little of what was her's in the first place.

"If so, doe sit undermine her philosophy (akin to everyone believes in God on the battlefield)? "
I once accepted unemployment benefits even though I was earning thousands of dollars a month. I told the state UI what I was doing. I was entitled to the benefits under the law. I have paid every cent of SUTA and FUTA. I'm required by law to pay. I certainly will accept every cent of benefits they offer me, even if I don't agree with the system. These critics want me to support the system and then reject benefits I'm legally entitled to under it.

She wrote an explanation of why those who oppose state largess are the only ones who are actually "entitled" to it. I tried to find a link for you because I know I've read that explanation somewhere, but I couldn't find it.