a mysterious advertisement without a gerund

We received a strange brochure in our letterbox today. It's from Australia Post and shows pictures of various computing devices for sale.

At the top it says: Part of me staying up to date.

Uhhh?

There's a picture of a man typing at a computer. I thought maybe his hands are the part of his body staying up to date. Or maybe his brain...

And then I wondered if the word 'staying' is a gerund, and not a present participle. Perhaps it means that having items of modern technology is part of his staying up to date.

To be quite honest, I hardly ever use a possessive pronoun before a gerund these days. Grammartips, at Homestead, gives these examples of incorrect use of the gerund:

He resents you being more popular than he is.
~Most of the members paid their dues without me asking them.
~They objected to the youngest girl being given the command position.
~What do you think about him buying such an expensive car.
~We were all grateful for Jane taking on the responsibility for the party.

I'd be likely in everyday speech to say these incorrect forms, rather than the correct forms:

~He resents your being more popular than he is.
~Most of the members paid their dues without my asking them.
~They objected to the youngest girl's being given the command position.
~What do you think about his buying such an expensive car?
~We were all sorry about Jane's losing her parents like that.

Sometimes, however, using the incorrect form of a gerund makes the meaning unclear. I think the brochure should say: Part of my staying up to date.