This is true. You cannot say with any certainty that Turkey had no impact. However, it also true that you cannot say with any certainty that Turkey will never join the EU. At present it is close to impossible but there are a number of conditions that have to be met for a country to be allowed to join the EU and it is perfectly feasible that with a regime change in Turkey to a more progressive and less dictatorial leader that they would meet the criteria if they wished.
We've had this discussion many times before. Turkey is the scare story but Romania, Bulgaria & Croatia are recent examples of countries joining, most likely against the UK public interest, without a referendum offered. There is no benefit to the majority of people on this country from adding on nations that are net receivers and that would be net immigrants to the UK and yet we failed to use our veto.
There is also no point having a veto if those in charge don't use it when the people want them to. I'm not saying the public would want them to use it to block the above mentioned countries joining, that's just a guess.
My position is similar to what
@indeedido mentioned earlier. There is a lot of good things in being part of the EU but I'd prefer to be trading partners instead of being part of a political union, particularly one where we are required to foot more than our fair share of the bill. There is no reason at all that we can't have a trade deal without being a member, just like Canada or Japan.