Yes, the Skills and saving throws mentioned in the Stat Block are the skills and saving throws which the beast is proficient at.
As your answer mentioned, the Skills subsection at (DMG 8) states that
The Skills entry is reserved for monsters that are proficient in one or more skills. For example, a monster that is very perceptive and stealthy might have bonuses to Wisdom (Perception) and Dexterity (Stealth) checks.
A skill bonus is the sum of a monster’s relevant ability modifier and its proficiency bonus, which is determined by the monster’s challenge rating (as shown in the Proficiency Bonus by Challenge Rating table). Other modifiers might apply. For instance, a monster might have a larger-than-expected bonus (usually double its proficiency bonus) to account for its heightened expertise.
The Saving Throws entry is reserved for creatures
that are adept at resisting certain kinds of effects.
For example, a creature that isn't easily charmed or
frightened might gain a bonus on its Wisdom saving
throws. Most creatures don't have special saving throw
bonuses, in which case this section is absent.
A saving throw bonus is the sum of a monster's relevant
ability modifier and its proficiency bonus, which is
determined by the monster's challenge rating (as shown
in the Proficiency Bonus by Challenge Rating table).
Oddly, though the BM section you mentioned states
Add your proficiency bonus to the beast’s AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in.
There seems to be no beast proficient at any saving throw, so I suppose this part is intended for homebrew content, future releases or just a mistake.