"Hun er bare sytti."

[gothicsquirrel]

Can this sentence also mean she is just (recently turned) 70 or just that she is only 70 (not older)?

[Deliciae]

It would only be taken to mean the latter.

For the former, you could say "Hun er knapt (barely) 70" or "Hun har akkurat fylt 70".

[effyleven]

Jeg er bare sytti, meg selv.

[lindsaype]

bare sytti...det er gammelt nok at hun kunne ha været barnevakt for Master Yoda!

[fveldig]

Det er gammelt nok til* at hun kunne * vært* barnevakt for Mester* Yoda

[Franskmann14]

Can we say "hun er kun sytti" ?

[Deliciae]

Yes, if this weren't a listening exercise that would be equally correct.