Can be true, yes.
If you provided your employer with a form P45 within that year from a previous job on which there were deductions, then he would be obliged to continue the scheme and issue a P60 at year end regardless of your working hours and rate of pay and regardless of whether he deducted any tax or NI from it.
Also, if the employer deducted any PAYE tax or NIC from your pay then again he is required to provide you with a form P60.
If you did not provide your employer with a form P45 then the employer should have provided you with a form P46 for you to complete, sign where appropriate, and hand back to him for processing. Unless on the form P46 you signed a declaration to the effect that this was your only or main job, then the employer would have been required to deduct basic rate tax from all pay, and hence a form P60 would be required. However, if you signed a declaration that it was your only or main job, AND you were never paid above the NIC Lower Earnings Limit (£97 per week in 2010-11) then the employer's statement is correct.