To the best of my recollection, I have never encountered a math journal which gave the author any input at all for choice of referees, nor betrayed any info about their identity. I sometimes have a guess that the referee may be the person who made the conjecture I am solving but I have never had confirmation, so to this day I do not know the identity of a single referee for any paper I have ever published. Indeed some of my papers have appeared without significant changes suggested but others have been completely rewritten to the point of doubling in length, due to added details, examples, clarification. One paper that had originally cited a number of "well known" results that were actually not published, expanded perhaps by a factor of 5 when all that material was meticulously included. When I have been a referee for a distinguished journal it was usually by receiving a paper from an editor whom I personally know or who was referred to me because of my record of publishing in the given area. Most of the time I know the editor from research contacts over the years. Often I know the author personally as well but I have never revealed to any of them that I was their referee, and I have not always accepted work written by acquaintances, if it seemed inappropriate for the journal. I think this is standard practice. Of course maybe other practices occurred and I was just unaware of them.
In the case of grant proposals to NSF, the author is now perhaps allowed to give a list of referees who should not be contacted, and perhaps in more recent times maybe also a list of potential referees, but one does not learn which ones are chosen, and the referees are contacted independently by the funding agencies. Besides, they are normally so well known that fakes would not be viable, i.e. full professors at elite schools. I have never submitted an email address for a potential referee but maybe such things occur now. I have been asked to serve on NSF granting committees, and they now meet together and discuss all decisions, after preliminary evaluation by the individual judges. I.e. one has to defend at least to some extent, granting recommendations, to ones peers.
Once I submitted a paper I rather liked to a top journal and after its being refereed the editor who was a friend of mine told me that while the paper was not considered high enough quality for the journal i submitted to, he was also editor of another less selective journal that he could guarantee acceptance to if I would agree to submit it there, so I did. On a few other occasions editors have solicited papers after learning of their content and before I had submitted them for refereeing. I assumed in those cases they would go out for refereeing, but that the editor obviously already had a favorable opinion of them. In a few instances I may have missed out on having them appear in more prestigious organs, but i bypassed the stress of submitting them, and in some cases benefited from being allowed to write them at greater length in a less selective journal than in one of greater demand.
On at least one case, a referee criticized my submission to a top journal as too long and as having an error, about which he was mistaken. Not wanting to shorten the paper I did not bother to explain the correct but questioned statements and resubmitted to a different excellent but slightly less exclusive journal. The editor sent it to the same referee who was upset I had not addressed his erroneous concern and rejected it again, but the kindly editor chose another second referee, obviously a specialist, who ignored the supposedly problematic statements but insisted we greatly shorten the paper and that it then be accepted. We never published the excised portions of the work but they became known informally from privately circulated copies of the manuscript..
Years later we received several requests for the material which we had been forced to remove and this material formed the foundation for several other publications by others, who even named those never published results after us. This was an odd experience, but in essentislly all cases I feel I was always treated with great fairness by referees and editors, and I support fully the concept of peer refereeing. Of course at the time I may have felt annoyed to have to rewrite a paper but in basically all cases the result was an imporved and more accessible work. In fact looking back I appreciate most the papers that were required to be improved before appearing.
In the modern nternet era there is a new phenomenon, of journals I have never heard of routinely emailing me with a request to submit papers, but I have always ignored these, as much in the category of proffered nigerian financial schemes.
As regards Springer, I have no first hand knowledge, but their reputation is slipping in the community, and I have read that ownership passed from an old school gentleman who felt publishing was a service to the scientific community into the hands of a publisher who wants to make as much money as possible by overcharging libraries for research subscriptions.
