They are right. It's not safe..
At best it's pointless..
At the moment, with my Oyster, when I get to a ticket barrier, I have to get the little plastic wallet out and swipe it over the reader. Takes a couple of seconds. I have an annual travelcard, which takes around 30 seconds to renew (thanks to TFL's website), but I only need to do that once a year then swipe the card..
If I switch to a NFC bank card, I have to either get my wallet out (not a good idea in some of the areas I travel to, even though I am rather large), or remove the card from my wallet. Both of which take longer than a couple of seconds.
I also have the problem that someone could run a reader over my card, and transfer money from my bank account.
Yes, I know about the limits, but I also know that it may take several transactions to trigger the security. Even if it does, bank security isn't always that reliable. Last year, when I renewed my travel card, the sudden large debit on the account triggered Santander's security and the transaction was declined. I got a text from the security system advising me to call a certain number.
The computer on the other end of the line confirmed the amount and told me it would allow the transaction. So, I went to my local branch. Their advice? Wait 48 hours to see if the transaction went through, then try again.
Thankfully, it didn't, else I would (temporarily at least) have been £1000 down. Something which I cannot afford.
So, as I am sure you can understand, I am not entirely convinced by the claims by the various authorities that NFC equipped bank cards are safe.
But, my main concern is safety. People have to get their Oyster cards out to swipe in some very dodgy places. If I get attecked and they take my Oyster card, yes, it will be incoveniant, but all I will have lost is whatever pay as you go balance I had on it (usually around £10) and a travelcard (which TFL will transfer to the new card anyway). No biggie, apart from it not being very nice if you have something stolen.
If I am attacked while swiping my bank card, they've potentially got access to my bank account. Not good at all.