Why seemingly assume a more competitive price is less safe? Perhaps they'd already erred on the high side?!
Asking only those who originally tendered lower sends a bad message. Why not an open tender, where those who tendered higher than Bristow get a look in?
I'm reminded of a story where an operator lost the bid, to be replaced by a contractor using 76s. The contractor found the 76 wasn't up to the task, and pilots were directed to use the transient limits in an endeavour to achieve what the tender had promised.