I find it more strange that when that phrase, "You will never be as happy in life as you are when in a relationship", is being thrown around, is often said by those in relationships that aren't... going well themselves. Mostly trying hard advertise that being in a relationship is the be all and end all of life itself rather than actually pointing out some home truths. Or maybe that's just me.
Personally, that phrase is used to overhype a relationship. Making it seem that it's all perfect and great and will make your life a lot more better if you have it then if you don't. Similar to the whole "If you don't have children, you will never know how it's like to be a real/complete woman" line. Suggesting that you better have this or do that, or your life is nothing and pointless. 7 billion people on this planet. We all have different motivations and goals.
I was young once, we all were, and we all thought about the person who we would go out with first. Your first date, first crush. Your first moment of feeling the difficult emotion of "love". We are at our best and on cloud 9. For the majority though that first relationship ends and for all, it would feel like the end of the world. Like nothing else matters because you felt a new sensation in your heart and mind, must now go away or be hidden deep inside. For some, it's something they get over in time and appreciate the feeling and moments they had when they had a special someone next to them. Learning and maturing into a different person. Having the understand that, well, this relationship didn't work, so I must try to move on in life and see what's out there and also find freedom and happiness on my own. Going down this path can lead to anything. I can't predict what would come of it.
However, you may have some people experiencing the opposite of what I said in the previous paragraph. Feeling like "the end of the world", is for them, the end of the world. They don't want to be on their own and only used to being dependant on someone else. Maybe, and I strongly say maybe here, the people in their lives that surround them growing up, may have influence them into thinking that being single is a shameful thing. That no matter how much your partner is a dick and an arse to you, it's best to be with someone that to be with no one at all. Yeah I know it may sound a bit over the top but it does happens. In certain religious groups, I often hear that the person you decide to begin a relationship with, no matter how old you are, you must think as far as marriage, because if you aren't thinking of marriage while you have been them for less than a week, then no point in dating them and being boyfriend/girlfriend. Sounds... extreme to me but maybe to others, it's not. I've only heard of one person who did that. What happened was they were a couple for about a year and a religious person they knew told them. "You are both a couple and are walking out in public as a couple but not married and that would bring shame to yourselves and family. Get married so no one can judge you." So they followed it. Until things went quite bad. The relationship fell apart badly. So in a normal situation you would think they should just divorce easily right? Unfortunately no. They can't because doing that would also bring shame to their family and themselves and mostly to the girl. They were around 19 by the way. Stuck in a difficult situation.
I have a few female friends and many times, through no fault of their own, end up in relationships that start out as great at first but then have their partners become a different person a week or few months later. More possessive, over engaging, judgemental, manipulative and the most common case, extreme jealously. Extreme jealously to the point where those new partners would tell (or instruct) their other half about who they should or shouldn't speak to, what to wear, and how to even speak and look when around others. That there is the power dynamic being switched from 50/50 to a scary 70/30, 80/20 or an even more scary 90/10. And if and when these relationships end for whatever reason, it may leave that person either being relieved to be single and put them off if relationships for a while, or in some cases a very long time, or have leave that person so emotionally scarred that the though of being on their own is too scary too process. Often times going into or back to a relationship that leads to the same story and ends with the same outcome.
TL;DR Each relationship is different and everyone should go at their own pace in building new relations. So in terms of the main heading, nah it's not completely true. Not by a long shot anyways. People can find happiness in anything. 7 billion people, 7 billion different motives and stories to tell and live through.
Sorry about the long read. I did go on a bit there