no its not illogical. we don't know how long lech was with polly. no one saw him prior.
Thats my point.
We dont know for sure, but we do have the testimony of Lechmere who says he saw her moments before hearing Paul and Paul who only says he sees him ahead.
No mention of how far away and no mention of any movement before he says Lechmere
Is coming towards him.
To be odd Lechmere must be there earlier than he claims. There is no reliable source which indicates that. Paul's 3.45 is not reliable.
Yes we can use the suggestion as the starting point for a theory, But witbout evidence it remains just that.