Neither Jane nor the Smith family know for sure that it was Madeleine.
Whether it was the same person carrying Madeleine or a different child, or different people carrying her, or different people carrying children who were not her ... it is still an open question as no one seems to have stepped forward to eliminate themselves.
A question: Why did the PJ not organise an e-fit of the person the Smiths saw?
The dogs showed no evidence, the DNA were inconclusive, no important fingerprints in the window ... Yes. Also that she was abducted by a stranger ...
But we do not coincide in some other aspects, Carana ... 
I think we can rely on three things based on the analysis of eyewitness testimonies:
1. Kate found the 5A window opened just after 22:00, just before raising the alarm.
2. Jane saw the abductor at 21:15 or 21:45.
3. The Smiths saw the abductor just after 22:00.
Heri.
About this theory that Tanner may have seen the abductor at 9.45pm ( at some other check ) rather than at 9.15pm
Are you saying you think she might have lied about seeing Gerry and Jez Wilkins at the same time as seeing the abductor ?
In eyewitness testimony there are more things than "true" and "lie" ... There is "false memory", for example, which can produce one thing to be "true" for the
honest witness, but "false" in objective reality.
A lot more you can learn reading Elizabeth Loftus, Robert Buckout, John Palmer, ... on eyewitness testimony.
I
only said that "based on the first testimonies of the 9 adults of the vacation group made on May 4th. 2007 (PJ main file pages 34 to 82), and the first testimony of Jeremy Wilkins made on May 7th. 2007 (PJ main file pages 494 to 505), and the second statements by Gerry, Matt and Jane on May 10th. 2007; and by Russell, Rachel Oldfield and Dianne Webster on May 11th. 2007 (PJ main file pages 891 to 903, 905 to 917, 919 to 931, 934 to 941, 943 to 947 and 949 to 954) it is not possible to conclude if Jane Tanner made her check at 21:15 or not (the only big inconsistency in the group testimonies, in my opinion). Also it is not clear to what extent the discussion of the events by members of the 9 adults group and the two timelines made by Russell O'Brien might have implanted false memories before the referred statements of May 4th. 2007. And it is not clear also if the group (except for Dianne Webster) discussion before the referred second statements, included in the files as a three pages printout (PJ main file pages 886 to 890) might have implanted false memories before the referred statements of May 10th. and 11th. 2007 . But it is only a small part of the statements made by the group. A more important thing, the sighting of a man with a child by Jane, is corroborated by the totally independent testimonies of the Smiths."
Heri.