My understanding is that underwater sounds can reflect back off the bottom and / or thermal layers in unpredictable ways. There are tales of submarines being tracked from more than a thousand miles away under the right acoustic conditions. I have no problem imagining that a pinger's signal could turn up three hundred miles away. Also, the only way I could imagine parts of the plane coming down 300 miles apart is if it was high up on re-entry al la space shuttle. I also can't imagine any fish making a love call on 37khz or so with a pulse repetition frequency similar to an underwater beacon.
And there is no reason to doubt the Chinese in this matter, unless you (or someone) dislike Chinese and are allowing that to cloud their judgement
This is the same signal.