It amazes me how many people get this wrong...It was actually From Me To You which got to number one in April 1963 whereas Please Please Me only got to number two in January of that year.
As far as I know, beale isn't wrong (unless anybody knows better). This question has come up before. The problem seems to be that, in the early 1960's, there were four different music charts on the go. "Please Please Me" reached number 1 on three of them. Unfortunately, the one in which it didn't reach number 1 is actually the chart used by the Guinness Book of Hit Singles (which, in turn, has been used by lots of other people). I don't know why this fourth chart was the one used.
No ! the answer you were given was right. It all depends on which chart you look at. The Guinness book of Hit Singles uses the Record Retailer as its source (and yes Please Please Me only reached No2 on that chart).
There were other charts in circulation at the time, and the NME chart (and others) say that "PPM" WAS a No1 for 2 weeks (23rd Feb and 2nd March 1963).