I've spent quite a bit of time in a wheelchair as a result of extensive leg surgery (eight surgeries in ten years). When we are on the right surface, particularly in mall corridors, grocery stores, etc., my DH and I have found a way for him to roll me along with him by holding my hand rather than pushing me. I use one hand to get myself started, and he holds my other hand to keep me up. It doesn't even look like he's pulling me! We love doing this because, honestly, I can't hear anything he says if he's pushing my chair from behind.
With that in mind, there's a good chance Liz Taylor has similar difficulties considering hearing often weakens with age.