One of my language partners sent me profiles of teachers who advertise as native speakers but whose profiles are littered with mistakes that not even a good B2 level student wouldn't make. So it is an issue. 

In my view, it would be an administrative nightmare for Italki to tackle this issue seriously.  It would probably need another employee working on the issue full-time and the benefits to Italki and students from this would be questionable.  The issue can probably be policed reasonably well within the Italki community itself by means of reviews and information-sharing.  

If a student feels that they have been ripped off by a teacher who exaggerated their fluency level, then they should complain to Italki.

It's not only here on Italki that self-evaluation is a problem ;  when looking for a course at a suitable level in adult education, you find that 'grade inflation' is rampant.  The tutors privately admit that a failure to administer proper tests to allocate [adult] students to the right level class makes it impossible to maintain the appropriate level of teaching, but seem reluctant to deter students who feel entitled to move up a level each year, whether or not they are ready to do so.

Here on Italki there are those who for nefarious reasons choose to declare themselves native speakers when clearly they are not.  Perhaps we should be more active as a community in 'outing' [exposing] such individuals.  It is very unlikely [though not impossible] that someone from India or the Philippines is a true native English speaker  i.e. has learnt to speak the language as their 'mother' tongue.

There is also a tendency to over-estimate ability on the part of many of us;  I felt obliged to downgrade my level in French when I came to realise that I was perhaps not as good as I had thought.  I also note that the C1 level here [4 bars] is labelled 'upper intermediate', rather than the 'advanced' level given elsewhere, but this also depends on whether you are using 'level already achieved', or level 'working towards' as the criterion for selecting your stated level.  This ambiguity leaves room for [unintended] error.

Like those who have commented above, I prefer to be cautious about my level, partly to avoid awkward situations.  Unfortunately, self-confidence is an important motivator in language learning, so it helps to be 'bullish' [over-confident] when it comes to self-assessment, and  'thick-skinned' about [insensitive to] the possible consequences.

Well, I do have a CPE passed so I see no reason to downgrade my level although I realise that a lot of people seem to think that one has the right to claim the C2 level if their English is perfect. Not even near-native good but ubernative perfect. This quasi-religious attitude towards some artificial scale where one's skills are judged based on, frankly speaking, nonsensical, highly standardised exam seems to be popular not only among language learners who attend courses based on this scale but also among self-study learners. Well, maybe it is understandable, who knows? However, since in the real exams one's level is actually judged based on four skills, of which italki members usually can witness only one or two, I would refrain from judging others.

And as for my level of Spanish, the bars match the level of the coursebook that I use at the moment. But I don't really care for the labels, which I probably should have mentioned at the very beginning of this post. I think that putting pressure on people in this regard will make them either underestimate their level out of fear for being judged or ridiculed or stop them from taking part in the discussions altogether, basically for the same reason.

So I'd say, let people claim whatever they want to claim.

But, the OOPT test italki offers is based on CEFR and they mention it here

https://www.italki.com/p/oet   

So I wouldn't be so sure that italki scale is not.