safeik brachos l'hakeil where there is a rov

Achronim discuss whether the rule of safeik brachos l'hakeil applies even where there is a rov to be machria the safeik.  (Is rov mevarer te safeik or is rov just a hanhaga, but the safeik remains?)   

The Rambam paskens (Meg 1:11):

עיר שהיא ספק ואין ידוע אם היתה מוקפת חומה בימות יהושע בן נון או אחר כן הוקפה קוראין בשני הימים שהן י"ד וט"ו ובליליהם. ומברכין על קריאתה בי"ד בלבד הואיל והיא זמן קריאתה לרוב העולם:

If a city has a safeik whether it is a mukaf or not, the megillah is read on both 14 and 15.  You would have thought that no bracha is recited since each reading is a safeik, but the Rambam paskens that a bracha is said on the reading of the 14th because  הואיל והיא זמן קריאתה לרוב העולם, there is a rov -- most cities are not mukaf and read on the 14th.  

QED that where there is a rov, the rule of safeik brachos l'hakeil does not apply.

Similarly, the gemara (Yevamos 121b) relates:

ההוא דהוה קאמר ואזיל מאן איכא בי חסא טבע חסא אמר רב נחמן האלקים אכלו כוורי לחסא

An aku"m went around asking if anyone knew the family of someone named Chasa, as he had drowned.  When he heard this, R' Nachman swore and said the fish have eaten Chasa.  

R' Akiva Eiger in the gilyon ha'shas quotes from the teshuvos of Hagahos Maimonis who questions how R' Nachman could take an oath using shem Hashem in this case.  Where someone falls into mayim she'ein lahem sof, a body of water that we cannot see the banks of, e.g. someone fell off a boat into the Atlantic Ocean, we assume his wife cannot remarry because there is always a chance that he emerged somewhere without our knowing -- i.e. there is a safeik.  So isn't R' Nachman's oath a safeik use of Hashem's name l'vatala?

The Hg"M explains that in most cases in fact the person will have drowned.  We have a rov that says R' Nachman's oath was not l'vatala.  It is just a chumra in dinei ishus that prevents the wife from remarrying despite the rov.  

QED again that using the shem Hashem, whether as an oath, or whether in making a bracha, where one has a rov to decide the safeik, is not a problem.

The common denominator between these cases is that the rov is a metziyus, it is based on facts on the ground.  A case were there is a machlokes ha'poskim and the majority of opinions favor one side, i.e. a rov of theories, may be a different animal entirely.