That's what is commonly believed, but that belief is actually wrong - other NATO members are obligated to - and I quote directly from Article 5 here - "(...) assist the Party or Parties so attacked by taking forthwith, individually and in concert with the other Parties, such action as it deems necessary, including the use of armed force, (...)"
The keywords here are "as it deems necessary" and "including the use of armed forces". There is no automatic need to send troops - if you as the attacked party think a strongly worded letter is all that is necessary, you just ask for that letter. Of course you can demand military support, but doing so takes time, and it is easy to consider a situation in which you do not have that time anymore.
For an application of that principle, see 9/11, when the US invoked Article 5, but which did not result in military action from all NATO members (several of which refused to take part in "pointless military adventures"). The US obstracized those countries, but ultimately (had to?) accept.