Is it necessary to add mentions such as "Any opinion expressed in the paper does not necessarily reflect the view of the funder"? I sometimes read in papers that the opinions, findings, and conclusion or recommendations expressed in the paper are those of the authors and do not necessarily reflect the view of the [funding agency name] in the acknowledgments section. E.g. in this paper:


  Stanford University gratefully acknowledges the support of the Defense
  Advanced Research Projects Agency (DARPA) Deep Exploration and
  Filtering of Text (DEFT) Program under Air Force Research Laboratory
  (AFRL) contract no. FA8750-13-2-0040 and the Defense Threat Reduction
  Agency (DTRA) under Air Force Research Laboratory (AFRL) contract no.
  FA8650- 10-C-7020. Any opinions, findings, and conclusion or
  recommendations expressed in this material are those of the authors
  and do not necessarily reflect the view of the DARPA, AFRL, or the US
  government


Is it necessary to mention this? If the authors omit such statements, does this mean that the opinions, findings, and conclusion or recommendations expressed in the paper do reflect the view of the funding agency?
It depends on the grant that you receive to do your work. Most if not all grants require you to acknowledge the granting agency. Some grants give you very specific language that you must use in your acknowledgement (ranging from the request to include the grant number and use the full name of the agency to very pedantic requests for particular wording).
And some grants do require you to specifically disclaim the granting agency from your conclusions and opinions. For example, NSF requires the following:

An acknowledgment of NSF support and a disclaimer must appear in publications (including Web pages) of any material, whether copyrighted or not, based on or developed under NSF-supported projects:

“This material is based upon work supported by the National Science Foundation under Grant No. (grantee must enter NSF grant number).”

NSF support also must be orally acknowledged during all news media interviews, including popular media such as radio, television and news magazines.
Except for articles or papers published in scientific, technical or professional journals, the following disclaimer must be included:

“Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.”


The NSF example is interesting because you don't need the disclaimer for academic journals -- presumably because the readers aren't presumed to be idiots.
In any case, this is all part of the grant letter that you receive when you get a grant -- and part of the contract you sign when you agree to receive their money. There may be other terms inside the grant contract that are not visible (rights of first refusal in licensing technology, etc.) but by their very nature, acknowledgements are the most visible.