is it true about eating re-frozen meat?

Perfectly fine to eat. The reason you want to avoid thawing and refreezing meat is that it dries out the steak, each time you freeze it the moisture inside crystallizes into little icey daggers and cuts the meat, then when you thaw the meat those tiny cuts make the meat bleed out more than it normally would, hence a slightly drier steak as moisture was lost. Fine to eat none the less.

You should be fine... to many freeze-thaw cycles can mush out the meat a little... or the steak will be a little drier than usual (due to moisture lost), but still should be good.

Also, you don't have to worry about food poisoning, especially if the steak was refrigerated or frozen throughout this accident.

If it was thawed out completely, bacteria will start to grow.

Re-freezing doesn't kill them, they just go dormant.

If it still had ice-crystals, it'll be safe enough.

The only thing I have ever noticed is that the texture wasn't quite right.