Doctors do have a higher divorce rate than average.
But anecdotally I know plenty of people who have had serious relationships during med school, a few who married while still students and many more who've got married since. Quite a number have medic partners, and it does cause difficulties with jobs etc, but people find ways of coping.
I got together with my now husband towards the end of my 4th year of med school (6 year course), having had a 2-year relationship prior to that. For the first two years of our relationship we were long-ish-distance as he (non-medic) was working in finance in London and I was still at uni in Cambridge, so we only saw each other at weekends. It was hard work, especially when I was away on placement, as I'd be away in DGH-land all week, come back to Cambridge Friday evening, pack and go straight to London, then get back from London on Sunday night, ready to head off to DGH on Monday again. I lived out of a suitcase for most of my 6th year! We moved in together after I graduated and I got an FY1 job in London, ended up staying there for 5 years. We moved out of London 6 months ago to start my registrar post, and he's got a job not too far away, so it's all worked out pretty well for us! My husband doesn't really understand what I do, (quote from him "But looking after ICU patients must be quite easy, because they're just asleep and not doing much") and is really squeamish so I can't discuss a lot of things with him, but he understands the demands on my time and how emotionally draining it can sometimes be.
Med school is tough, but contrary to some people's belief, you don't have to be an antisocial hermit to get through it.