I have read this thread, and the previous ones, I do not usually comment on such things however I would like to give some insight into how "witnesses" to events are not always correct in what they report. My job can involve asking a number of people about certain events, it is a known issue that people differ in what they saw and report, there is no malicious action involved, it is purely how people behave.
I have been in the situation of asking very professional people to describe an event, I can receive very differing reports, to the point when it becomes almost impossible to know what is correct. Added to that, some people are easily influenced by the people questioning them, therefore providing the answers they "think" those people want to hear.
So in this situation, the differing narratives as to where the mobile phone was, could purely be the witness or witnesses, believing it was on the bench, but if a police officer then asks "are you sure it was no on the floor?" a witness then may answer " thinking about it, the phone may have been on the floor".
This scenario is a know issue when gathering information, so unless there are photographs or CCTV to confirm a situation, it is known that witnesses do not always provide 100% correct information as to what happened. It could be what it happening to cause the differences in reports as to the timeline and what happened?
Moving on the the police actions (this is not a criticism of Lancs police), they are only human, some humans will stick very to an initial opinion and not deviate from that opinion no matter what, others will be more open to outside help. The situation with the other search team, is it a case of the police had their feather ruffled and only allowed a small amount of "help" from him, with opinions differing as to if a body was in the water and if so, if it would be found?
A different force may have been more open and appreciated an external opinion and help? The sudden departure of the search team may explain the situation being the former rather than the latter?
In many professional environments having information means you can control the situation, if you do not have the information, sometimes behaviour is affected to the extent outward actions come across as though information is being held back, in order to protect the belief in only one scenario and the lack of proper information to confirm it. It can almost be an act of self protection.
I have certainly come across many professionals who will stick like glue to a scenario rather than allow others to assist or provide an alternattive narrative, on the other hand I have worked with many professionals who will consider anything and are very much a "say what you think, no matter how ludicrous it sounds, as it may help".
Moving on, I have looked at the latest available ONS stats on suicide - for women 45% are by hanging or similar, deliberate drowing is only the 4th most common method of suicide and is a very low percentage.
Finally, add in the media and I am not surprised there is an element of differing information being available and sometime Lancs police looking like they are witholding information (they may be for good reasons). I think the statement "we believe the most likely scenario is this was an accidental slip into the water with subsequent drowing, the reasons for this are X,Y,Z. We will pursue that opinion because of X,Y and Z but of course will always keep an open mind to other scenario, but the information we have means other scenario are unlikely" would have been better received and caused less speculation.